The millennium is a 1000 year period where believers will rule and reign with Christ on the earth as a reward for their faithfulness.
Some people believe that we are in the millennium now and therefore that the second coming of Jesus will be after the millennium. They are called 'post-millennialists'.
Some people believe that the millennium does not refer to a literal period of time but rather that it is symbolic of the entire period between the first and second comings of Christ. In other words, we are living in the millennium period now. They are called 'a-millennialists'.
Still others believe that the second coming of Christ will occur before the millennium. They are referred to as 'pre-millennialists'.
The challenge for all interpreters is that Revelation 20 is the only explicit reference of the millennium in the New Testament and there is no mention of the relation of the second coming to the millennium in the actual text (whether it is before or after).
Personally, I don’t think we’re in it now (you call this rest?). I tend to think that the second coming will occur first and then the millennium will be after that, but even that view has some challenges. So, this is not a subject anyone can be dogmatic about because there are too many unknowns.
P.S. For an overview and discussion of each of the major views about the millennium see the book Three Views of the Millennium and Beyond (Darrell L. Bock: General Editor). Another book on this topic that may interest you is the The Christian Millennium by my dad, Kevin J. Conner.