The binding of Satan in Revelation 20 has always been a major issue of debate between premillennialists and amillennialists. Premillennialists, like me, insist on the chronological nature of chapters 19-20. So the second coming of Christ in Revelation 19 precedes the 1000 years of Revelation 20. Amillennialists, many of them following the Augustinian recapitulation view of the literary structure of the book of Revelation, argue that Revelation 20 begins over again with a discussion of the present age. Hence, the 1000 years (as an indefinite period of time) describes the present or Church age. This means that the binding of Satan described in Revelation 20 is happening now at the present time.
Consequently, there is a debate between premillennialists and amillennialists over the activity of Satan during the present time. For example, in the excellent book (in my view) Competent to Counsel by Jay Adams, he honestly affirms that, because he is an amillennialist, he does not recognize demon possession when he counsels people. Now, his views as well as others, always get qualified in later writings or expressions, but the sentiment is generally a limitation of Satan’s activity in the present age.