Who are the seven kings mentioned in the book of Revelation?
From Revelation 17 (KJ21):
10 And there are seven kings: five are fallen, and one is, and the other has not yet come; and when he cometh, he must continue a short space.
11 And the beast that was, and is not, even he is the eighth, yet is one of the seven and goeth into perdition.
Who are these seven kings, that precede Satan?
Here's a decent analysis of the passage.
It is these seven kings that we want to deal with in this paper. Basically, there are three different interpretations that could be considered about who these seven kings are:
Seven Individual Kings: This interpretation has a couple variations. Some try to identify seven individual emperors (a typical preterist view), and others seven individual popes.
Seven Kingdoms: This interpretation typically identifies the first five kings either as being Babylon, Medo-Persia, Greece, Pagan Rome, and Papal Rome; or as being Egypt, Assyria, Babylon, Medo-Persia, and Greece.
Seven Forms of Roman Government: This interpretation typically identifies the first five kings as being five of the following forms of government: a) kings, b) consuls, c) dictators, d) decemvirate, e) military tribunes with consular power, and f) triumvira
And all of these assume that Revelation was speaking to the contemporary church (for what it's worth, I believe this also.) However, millennialist/apocalyptic sects of Christianity generally assume that Revelation is a prophecy of the End Times, and so the interpretation of the seven kings/kingdoms has been adjusted throughout the centuries to include whichever powers make the prophecy feel most urgent; for example, when I was growing up in the SDA church in the 80s, the last two kingdoms were the Soviet Union and the USA.
@MT_Head I'm not sure how interpretations that mentions popes or papal Rome could be spoken to the contemporary church (if by contemporary you mean contemporary to the book of Revelation)