Eschatology, which means “study of the last things” and oddly enough it is usually the topic Christians avoid and study last b/c it is so difficult. Though I am a dispensationalist, this post is not intended to be an argument for either side, rather a simple orientation so we can have a better idea of what each side believes. Hopefully, this post will help out some other confused individuals out there.
I. Covenant Theology (CT)
The basis of CT is the idea that, as William VanGemeren puts it, “Single plan of God, confirmed in the one mediator Jesus Christ”. 
This via 3 Covenants:
1) The Covenant of Grace
God has one plan of salvation , one mediator, and one eschatological plan all men share. 
2) The Covenant of Redemption
A specific agreement between the Father and the Son that they would exalt each other in the following way: the Father would honor the Son by sending him to save lost sinners through a penal self-sacrifice leading to a cosmic reign in which the central activity would be the imparting to sinners through the Holy Spirit of the redemption he won for them; and the Son would honor the Father by becoming the Father's love-gift to sinners and by leading them through the Spirit to trust, love and glorify the Father on the model of his own obedience to the Father's will. 
3) The Covenant of Works
Whereby God undertook to prolong and augment for all subsequent humanity the happy state in which he had made the first human pair -- provided that the man observed, as part of the humble obedience that was then natural to him, one prohibition, specified in the narrative as not eating a forbidden fruit. The penal sanctions of which was the loss of good and corruption of nature. 
II. Continuity Between the Two Testaments
CT sees a more continuous relationship between the two testaments. This stems from the idea of God having a singular plan (ie the 3 Covenants) for His elect.
1: The Tale of Two kingdoms: The Kingdom of God vs the Kingdom of Satan
Dr. John Currid of RTS would like for us to view the Bible with “Seed theology,” that is through an unfolding of the story between the Seed of the Woman and the Seed of the Serpent.  This starts from Genesis 3:15 and thus the world history as well as the Bible’s story is one that should be seen in a redemptive-historical perspective.
2. Supersessionism: Israel and the Church are one
The Church has superseded Israel and some view Israel as a type of the Church. One of the major motivating factors of this is that God has one Kingdom who He has given the Covenants to and thus He only has one people the Church.
3. Continuity between the Law of Moses and the Law of Christ
God gives His law to his covenanted people to establish a personal bond. The Law of Moses and the Law of Christ are not different. However, under Christ. the law is newly administered and more deeply expounded. There is discontinuity in its form or shape, but not in its essence. 
4. The Content of Faith
Though both camps believe that the saving work of Jesus Christ is the basis of all salvation, CT believes that ever since Adam and Eve, the content (not basis) of saving faith was the gospel - the message that Jesus Christ would be the redeemer. Though, it was not as fully known to all, it has been the basic message of Jesus Christ as the Savior that saves throughout all generations. 
5. The Conditionality of the Biblical Covenants (Abrahamic, Davidic, etc.)
As a gross generalization, CT sees the Biblical covenants as conditional and dispensationalists see them as unconditional.
III. Hermeneutics of CT
Three hermeneutical beliefs 
a. Precedence of the NT over the OT
b. National Israel as a type for the Church
c. Nonliteral fulfillment of OT texts
IV. Views on The Millenium
Note: When Christians talk about amillennialism, postmillennialism, and premillennialism, the point of reference is the second coming of Jesus Christ, not the Rapture. So a “premillennialist” would believe that the second coming is before the millennial kingdom, “post” would be believe that Jesus is coming after the millennial kingdom (though they do not believe in a literal 1,000 year kingdom), and “amillennialist” would not believe in an earthly millennial kingdom. I mention this b/c this is often confused with the terms “pretribulation”, “midtribulation”, and “postribulation” which refer to the timing of the Rapture, not the second coming.
i. Amillennialism 
1. Promises to Israel are spiritual and typical
2. Promises are fulfilled in Christ's reign of the Church now and in the eternal state.
3. Israel has lost their privilege
4. Some believe there will be a large in pouring of Jewish believers one day.
ii. Postmillennialism 
1. Gospel will be spread through out the earth and spiritual and material blessings will come to all people. Then Christ will come.
2. Promises to Israel are spiritual and typical
iii. Non-dispensational Premillennialism 
1. Literal 1,000 year reign of Christ, but without a specific Jewish Emphasis.
2. +/- a great ingathering of Jewish believers, but not a restoration of the nation-state of Israel.
V. Timeline of History
Both CT and dispensationalism separate the world’s history into different eras. Klooster a CT, has divided history into the following categories: 
a. Covenant of Works
b. Covenant of Grace (protoevangelion)
c. Start the Seed of the serpent vs Seed of the woman
2. The Fall and Two Kingdoms
a. Cain vs Abel
3. The Flood and Babel
a. The sons of God and the sons of men intermingling, endangering the promise in Gen 3:15 and the Kingdom of God (remember by then only Noah was righteous), therefore God sends a flood to wipe out the kingdom of the serpent.
b. The Noahic covenant was not a new dispensation, but an elaboration of the ruling task of Adam, now in a postdiluvian (postflood) era.
a. The kingdom of the serpent in a new apostasy, however God promised never to flood the earth again. So He confuses their language.
b. End of ethnic universalism
c. Pentecost is the redemptive counterpart, where all the nations are now united via Christ.
4. Abraham and the Patriarchs
a. God's Kingdom is now moved onto Abraham and Israel
b. Abraham and Israel are chosen by God to birth the Redeemer-King.
c. The diversity of God's actions promotes one redemptive program.
d. Institution of the First Sacrament - Circumcision (looks forward to Christ)
5. Theocratic Kingdom of Israel: Exodus to the end of the OT
a. Institution of the Second Sacrament - Passover (looks forward to Christ)
b. Moses as covenant mediator with Israel parallels Christ as covenant mediator with the Church.
6. Inauguration of the Messianic Kingdom
a. All the covenant promises fulfilled in Christ.
b. With the veil torn the Levitical (Phineas) covenant was fulfilled.
c. New covenant starts
d. The new sacraments of baptism and communion instituted (looks back at Christ).
7. Pentecost to the end of the NT
a. The Church is not a parenthesis, but an administrator of the covenant sacraments and keeper of the keys of the Kingdom.
b. Already and not yet aspects of the Kingdom.
c. Christ is ruling right now.
8. The second coming and the consummation of the Kingdom
a. The Kingdom of Christ will win over the World and than Christ will come.
I. Dispensationalism (D)
One of the most often quoted and influential members of Dispensationalism (D) is Dr. Charles Ryrie who says there are three necessary conditions for D: 
1) The distinction between Israel and the church
2) The usage of a system of literal hermeneutics
3) The belief that the underlying purpose of God in the world is to produce his glory.
Dr. John Feinberg gives us a more in depth analysis of the essentials of D. 
A. Recognizing multiple senses of words like "Jew," "Israel," and "Abraham's seed."
i. These are used in a genetic, political, spiritual, and typological sense and no sense is more important (especially spiritual) or cancels another.
i. The progress of revelation and the OT vs NT priority:
CT as we have seen, read the OT reinterpreted in light of the NT, but this is vice versa for Dispensationalism. NT has priority for CT b/c the OT was the shadow and NT the fulfillment, so the claim that you should take the clear revelation (NT) to understand the hidden (OT). D believes that the promises of the OT (ie to Israel) are clear and not all typological and remain unfulfilled in the NT. Therefore they are not canceled b/c unconditional promises of God can never be canceled.
ii. NT use of the OT, and typology.
Types are not allegories or symbolize that lose their meaning later. Types are rooted in historical facts. The NT writers never explicitly say that they cancel out the original meaning and different NT writers use the same OT verses differently. Double or multiple fulfillment of certain prophecies are the issue here, not their cancellation.
C. Unconditionality of the Biblical covenants (Abrahamic, Davidic, etc.).
Covenants are not only spiritual, but social, economic, and political as well. They can extend to others (ie New Covenant onto Gentiles), but its primary fulfillment is to Israel. One should not emphasize only one aspect of the covenant (ie spiritual) at the expense of the other aspects.
Again, as a gross generalization, C sees the covenants as conditional and D as unconditional.
D. Distinctive future for ethnic Israel
1. A belief in premillenialism with a distinctive Jewish emphasis is prominent
2. OT and tribulation saints are part of the Kingdom
3. Some believe the fulfillment is all in the future (classical D) and others believe some spiritual aspects are happening now (progressive D) ie the Kingdom here/now hypothesis.
E. The Church is a distinctive organism (from Israel) that began at Pentecost and is united with Christ.
F. Philosophy of History
The more one stresses redemptive history to the exclusion of God's other work, the more one is C. The more one stresses God's multi-faceted work in history, the more one is D.
G. Things Not Essential to Dispensationalism
a. Dispensations are not essential to dispensationalism
b. The idea that each dispensation is a test and failure nor the number of dispensations one holds is not essential
c. Calvinism or Arminianism
d. One's understanding of the law
e. A belief in multiple ways of salvation (This is in fact a misunderstanding of D thought and emphatically denied by many). 
II. Discontinuity Between the Two Testaments
As we can see from the essentials, D sees a more discontinuous relationship between the two testaments.
1: The Tale of Two People: Israel and the Church
D believes that God has two separate programs: one for Israel and one for the Church. The predominant view is that God used Israel from Abraham until Pentecost. From Pentecost to the Rapture, God will use the Church. After the Rapture, God will restart His program with Israel and His promises for Israel will come to fruition in the Millennial Kingdom.
2. Nonsupersessionism: Israel and the Church are separate
From what we have said so far, it should come to no surprise that D does not believe that the Church has replaced Israel or that Israel was a type for the Church.
3. Discontinuity between the Law of Moses and the Law of Christ
D believes that the Law of Moses was temporal in its nature and fulfilled (thus abrogated) with the coming of Christ. Thus, NT believers are no longer under the Law.
4. The Content of Faith
To quote John Feinberg:
The ultimate object of faith in any and every age is God Himself. The ultimate issue at any time in history is whether a man will take God at His word and exercise faith in the provision for salvation which God reveals… it is important to remember that since in each economy the content is what God has revealed, belief in the content for that age is belief in the ultimate object of faith. 
So those who adhere to D, say that though Jesus was the basis/grounds for all salvation, people in the OT could not have known about Jesus b/c God did not reveal Him until the NT times. Therefore, people in the OT were still saved by faith in whatever God had revealed to them up to that time, for how could they believe in someone they never heard about?
5. The Unconditionality of the Biblical Covenants (Abrahamic, Davidic, etc.)
As a gross generalization, CT sees the Biblical covenants as conditional and dispensationalists see them as unconditional and yet to be fulfilled.
III. Hermeneutics of D
Four hermeneutical beliefs 
a. Belief that OT texts need to be interpreted in their own right and not reinterpreted by the NT
b. Progressive revelation does not cancel unconditional promises to Israel
c. National Israel does not function as a type that is transcended by the Church
d. OT promises can have a double fulfillment or application with both Israel and the Church
IV. Views on The Millenium
D believes in that the second coming of Christ is before the start of the millennial kingdom and that it is a literal 1,000 year reign of Jesus Christ on the earth before the eternal state. Important to this idea, as previously mentioned, is that it is the fulfillment of many promises made to the nation of Israel (ie the restoration of their land, preeminence among the nations, kingship of the Messiah, etc.)
To quote Dr. Arnold G. Fruchtenbaum:
While it is true that the millennium (that is, one thousand years) is found only in Revelation 20, the belief in the Messianic Kingdom does not rest on this passage alone. In fact, it hardly rests on it at all. The basis for the belief in the Messianic Kingdom is twofold. First: there are the unfulfilled promises of the Jewish covenants, promises that can only be fulfilled in a Messianic Kingdom. Second: there are the unfulfilled prophecies of the Jewish prophets. There are numerous prophecies of the Old Testament that speak of the coming of the Messiah Who will reign on David’s Throne, and rule over a peaceful Kingdom. There is a great amount of material in the Old Testament on the Messianic Kingdom, and the belief in a Messianic Kingdom rests on the basis of a literal interpretation of this massive material.
Also, the idea of the rapture and a seven year tribulation is prominent within premillennial eschatology and though there is some disagreement as to the timing of the rapture.
i. Pretribulational rapture
Rapture occurs before the tribulation b/c the Church is supposed to be saved from the wrath of God that He pours out during those seven years.
ii. Midtribulational rapture
Rapture occurs at the halfway point of the tribulation. The severity of the later half of the tribulation is much greater and is even called the “great tribulation” and this is what the Church is saved from.
iii. Postribulational Rapture
Rapture occurs after the tribulation, as the saints are supposed to be tested through the seven years of tribulation.
V. Timeline of History
D generally divides biblical history into different dispensations. Dispensations are defined by the Scofield Reference Bible as "a period of time during which man is tested in respect of obedience to some specific revelation of the will of God. Seven such dispensations are distinguished in Scripture." Dr. Charles Ryrie has noted that this has caused some confusion and defines it as:
“A distinguishable economy in the outworking of God's purpose.” 
There have been seven classical dispensations, which I believe were first described by CI Scofield. Here they are:
The Seven Classic Dispensations (Red are my inserts) 
1. Innocence (freedom) - Edenic covenant
This is the time before the Fall in the Garden of Eden, where Man’s responsibility to God was not to eat from the tree of Good and Evil.
2. Consciense (moral responsibility) - Adamic covenant (protoevangelion)
By the fall, Adam and Eve acquired and transmitted to the [human] race the knowledge of good and evil. This gave conscience a basis for right moral judgment, and hence the race came under this measure of responsibility-to do good and eschew evil. 
3. Human government - Noahic covenant
Out of the fearful judgment of the flood God saved eight persons, to whom, after the waters were assuaged, He gave the purified earth with ample power to govern it. This, Noah and his descendants were responsible to do. The dispensation of human government resulted, upon the plain of Shinar, in the impious attempt to become independent of God and closed in judgment: the confusion of tongues. 
4. Promise (patriarchal rule) - Abrahamic covenant
Out of the dispersed descendants of the builders of Babel, God called one man, Abram, with whom He enters into covenant.  God moves specifically to work through one man’s descendants.
5. Law - Mosaic/Sinatic, Palestinian, (Levitical/Phineas), Davidic, New covenants
With the introduction of the Law, there is major shift in how God is dealing with man. Now, mankind is obligated to follow the specific regulations contained within the Mosaic Law.
*Christ's Earthly Ministry
Jesus describes this time as unique and one where there should be “no fasting while the bridegroom is there.” Besides, it should go without say that due to Jesus’ physical presence on earth there is a different economy between God and man (eg. whatever He said was authoritative and must be followed). In addition, specific economic shifting events such as the rejection of the Messiah by Israel and His death and resurrection occurred during this time.
The authority of Christ was laid upon the Apostles and they spoke infallibly in regards to the faith. This period is also marked by the miraculous sign gifts working prolificially within the layity of the Church and the writing of the NT.
6. The Church, Grace (Mystery Parenthesis)
Our current age that is between God’s program for Israel. God is now using the Church to spread salvation and the Kingdom into the world.
7. The Kingdom (Millenial Kingdom)
The return of Christ on Earth with the whole world under his reign. Israel has prominence among the nations, though the whole world is now at peace and full of blessing. Although sin, unbelief, and death are weakened, they are still in existence.
*The Eternal state
God now dwells among His saints (cf. Rev 21:3). The the New Heavens, the New Earth, and the New Jerusalem are ushered in. Finally, sin and death are no more and all His saints will now be forever glorified and directly be with Him for all eternity.
VI. Progressive Dispensationalism vs Classcial Dispensationalism
Currently, there is much discussion within dispensationalism. Much of this centers around the idea of progressive dispensationalism that was made popular by Drs. Darrell Block, Craig Blaising, and Robert Saucy. Though this may be a little off topic, I believe it is important to understand the difference between the two. Rev. Jack Brook has an excellent summary of the major differences between the two views: 
1. One plan of salvation: There is only one plan of redemption, not one for Israel and a different one for Christians. There is only one New Covenant, not two. The redemptive plan is revealed through God’s covenants. It begins with Abraham’s covenant, which combines physical and spiritual promises. David’s covenant, as developed by the later prophets also has redemptive application, since the Savior would be the Son of David. The New Covenant obtains redemption in fulfillment of the Abrahamic and Davidic. The redemptive plan is holistic, not manifold.
2. Four dispensations: There are four dispensations:
- Ecclesial (Church)
- Zionic (subdivided into millennial and eternal-kingdom phases.)
3. One people of God: The Christian Church is quite distinct from Israel, but not radically distinct. The Church is not a mere “parenthesis” in an otherwise-Jewish divine plan. The Church is not “Plan B”. It is not a separate category of humanity, in the way the Bible speaks of Jews or Greeks. There is continuity between the Church and Israel, not discontinuity alone. All believers from all dispensations are united in one general assembly in heaven (Hebrews 12.)
4. Complimentary hermeneutics: The old claim that a consistent grammatical-historical method of interpretation will always produce traditional dispensationalists is demonstrably untrue. The NT doesn’t follow Charles Ryrie’s definition of “consistent literalism” in the way that it handles OT prophecy. The NT often expands upon the OT prophecies, without contradicting their original contexts. Implications are developed from words which were not developed in the OT. PD calls this a “complementary” hermeneutic: The NT adds onto the OT prophecies in a way complementary to their original context.
5. Already/Not Yet: The Kingdom of God’s blessings are mostly reserved for Christ’s second advent, but parts of it are manifested today through the Holy Spirit. The geo-political aspects will occur in the future. The Church is grafted into some key aspects of the New Covenant (justification, the gift of the Spirit, resurrection hope), but the geo-political features for Israel have not yet happened.
6. Davidic Reign Now: Christ’s Davidic reign began in part when He ascended to the right hand of the Father. Some of the Davidic promises have been fulfilled, many others must wait until Christ returns. Salvation blessings are mediated to us through Jesus, who fulfilled Psalm 110:1-2. “Christ” and “Son of God” were both Davidic titles. Jesus’ priesthood is that of Melchizedek, an office originally given to David. Jesus’ Davidic kingship was the method by which God would fulfill all of His promises to Abraham (Luke 1:55)
 Vangemeren, Willem. “Systems of Continuity.” In Continuity and Discontinuity: Perspectives on the Relationship Between the Old and New Testaments. (Westchester, IL: Crossway Books, 1988), 37-62.
 Packer, JI. Gospel Pedlar. INTRODUCTION: ON COVENANT THEOLOGY. Cited 04 Feb. 2009. <http://www.gospelpedlar.com/articles/Bible/cov_theo.html>
 Currid, John. Judges through Poets [Online Lectures]. Retrieved from http://itunes.rts.edu audio lectures.
 Chamblin, Knox. “The Law of Moses and The Law of Christ.” In Continuity and Discontinuity: Perspectives on the Relationship Between the Old and New Testaments. (Westchester, IL: Crossway Books, 1988), 181-202.
 Klooster, Fred. “The Biblical Method for Salvation: The Case for Continuity.” In Continuity and Discontinuity: Perspectives on the Relationship Between the Old and New Testaments. (Westchester, IL: Crossway Books, 1988), 131-160.
 Vlach, Michael. “The Church as a Replacement of Israel: An Analysis of Supersessionism.” Ph.D. dissertation, Southeastern Baptist Theological Seminary, 2004.
 Feinberg, John. “Systems of Discontinuity.” In Continuity and Discontinuity: Perspectives on the Relationship Between the Old and New Testaments. (Westchester, IL: Crossway Books, 1988), 63-88.
 John S. Feinberg, “Salvation in the Old Testament” Tradition and Testament. Essays in Honor of Charles Lee Feinberg. Chicago: Moody Press, 1981. Hbk. ISBN: 0802425445. pp.39-77.
 Fruchtenbaum, Arnold. Pre-Trib Research Center. Premillennialism in the Old Testament. Cited 04 Feb. 2009. <>
 Ross, Allen. “The Biblical Method for Salvation: The Case for Discontinuity.”In Continuity and Discontinuity: Perspectives on the Relationship Between the Old and New Testaments. (Westchester, IL: Crossway Books, 1988), 161-180
 Brooks, Jack. EndTime.org. Progressive Dispensationalism: What is it? Cited 04 Feb. 2009.
 Ryrie, Charles. Biblecentre.org. What Is a Dispensation? Chapter 2 of "Dispensationalism" Cited 04 Feb. 2009. <http://www.biblecentre.org/topics/ccr_2_dispensationalism.htm>
 Socfield, CI. Biblecentre.org. THE SEVEN DISPENSATIONS. Cited 04 Feb. 2009. http://www.biblecentre.org/topics/cis_rd_2_seven_disp.htm