The future promised advancement of the Kingdom of Christ is an event unspeakably happy and glorious. The scriptures speak of that time, as a time wherein God and His Son Jesus Christ will be most eminently glorified on earth.
Edwards believed that that last thousand years (or so) of the church age would be the millennial period, and it would a period of great triumph for the church on earth. Since he believed it would be substantively better than the present state, it is fair to say that he did not believe it had yet begun. The consequence of this position is both profound and immediately evident: Edwardsian type postmills are almost alone among Christians in thinking that the Second Coming is still in the distant future. While they (we) may hope that Christ returns today, and strive to live as though he may, (who knows, we might be wrong) the scriptures seem to indicate a glorious promise of success for the Church that has not yet occurred.
Charles Hodge is another renowned theologian and postmillennialist. He wrote:
As therefore the Scriptures teach that the kingdom of Christ is to extend over all the earth; that all nations are to serve Him; and that all people shall call Him blessed; it is to be inferred that these predictions refer to a state of things which is to exist before the second coming of Christ. This state is described as one of spiritual prosperity; God will pour out His Spirit upon all flesh; knowledge shall everywhere abound; wars shall cease to the ends of the earth, and there shall be nothing to hurt or destroy in all my holy mountain, saith the Lord. This does not imply that there is to be neither sin nor sorrow in the world during this long period, or that all men are to be true Christians. The tares are to grow together with the wheat until the harvest. The means of grace will still be needed; conversion and sanctification will be then what they ever have been. It is only a higher measure of the good which the church has experienced in the past that we are taught to anticipate in the future. This however is not the end, After this and after the great apostasy which is to follow, comes the consummation.
Edwards and Hodge represent the two major divisions within postmillennialism (leaving the question of reconstructionism and preterism aside). While all postmills, by definition, agree that Christ will return after the millennium, and while all postmills are optimistic about the future of the world and the Church’s position therein (a view unique to that eschatology), some (Edwards) hold that the millennium hasn’t yet commenced, and that it will be quite distinctive from the present state. Others (Hodge) believe that the millennium began at the first advent. In a sense, the latter are distinguished from amillennialists only by their optimism that before Christ returns a large part of the world will be converted.
1 Much of this discussion comes from Postmillennialism, An Eschatology of Hope, Keith A. Mathison, P&R Publishing, 1999.