As far as the millennium goes, we tend to agree with Augustine and, derivatively, with the amillennialists. The Catholic position has thus historically been "amillennial" (as has been the majority Christian position in general, including that of the Protestant Reformers), though Catholics do not typically use this term. The Church has rejected the premillennial position, sometimes called "millenarianism". In the 1940s the Holy Office judged that premillennialism "cannot safely be taught," though the Church has not dogmatically defined this issue.
With respect to the rapture, Catholics certainly believe that the event of our gathering together to be with Christ will take place, though they do not generally use the word "rapture" to refer to this event (somewhat ironically, since the term "rapture" is derived from the text of the Latin Vulgate of 1 Thess. 4:17—"we will be caught up," [Latin: rapiemur]).
Many spend much time looking for signs in the heavens and in the headlines. This is especially true of premillennialists, who anxiously await the tribulation because it will inaugurate the rapture and millennium.
A more balanced perspective is given by Peter, who writes, "But do not ignore this one fact, beloved, that with the Lord one day is as a thousand years, and a thousand years as one day. The Lord is not slow about his promise as some count slowness, but is forbearing toward you, not wishing that any should perish, but that all should reach repentance. . . . Since all these things are thus to be dissolved, what sort of persons ought you to be in lives of holiness and godliness, waiting for and hastening the coming of the day of God, because of which the heavens will be kindled and dissolved, and the elements will melt with fire! But according to his promise we wait for new heavens and a new earth in which righteousness dwells. Therefore, beloved, since you wait for these, be zealous to be found by him without spot or blemish, and at peace" (2 Pet. 3:8–14).
