The common view of critical scholarship is that the Revelation is a Jewish apocalypse, written circa AD 90-100. The beast which comes from the sea (chapter 13) or abyss (chapters 11, 17) is a symbol for the Roman Empire of the author's day. The seven heads of the beast, which 'are seven kings', somehow represent Roman emperors.
By the late first century, the Nero Redivivus myth had emerged. In AD 68 the emperor Nero was declared an enemy of the empire. He subsequently stabbed himself in the neck and died, and he was quickly buried. But rumor arose that he hadn't really died, but escaped to Parthia out east. Or perhaps he had died, but would come back from the dead. Either way, it was said he would one day return with an army from beyond the Euphrates to conquer Rome. This myth received moderate acceptance by Jews and Christians alike, and can be found in apocalyptic texts like the Sibylline Oracles.
Today's scholars believe the Nero Redivivus legend is reflected, in part or in whole, in a handful of passages in the Revelation. Chapter 9 mentions an immense army coming from the east, beyond the Euphrates. Chapter 13 has one of the beast's seven heads (which symbolize seven kings) fatally wounded by a sword, followed by the beast's unexpected recovery. Chapter 16 again mentions armies from beyond the Euphrates gathered for war (though here it seems to be Rome doing the gathering). Chapter 17 mentions how one of the beast's kings 'was, is not, and will come'. And of course, the number of the beast's name in chapter 13 is six hundred sixty-six, which equates to 'Nero Caesar' in gematria.
After that, the biggest contention is whether the revelator meant or cared to identify any other emperors. The argument against is that the number seven is simply symbolic, meant to represent the idea of the emperors, with Nero being singled out because he was the first to actually instigate a persecution of Christians in AD 64. However, the trend in apocalyptic literature has the authors thinking of specific rulers. Daniel 11 never names names, but is otherwise an obvious recap of specific kings of the Seleucid and Ptolemaic dynasties. Fourth Ezra 11-12, written contemporary to the Revelation, symbolizes the Roman Empire as an eagle, and goes into detail about how its wings and feathers correspond to the line of emperors, going back to Julius Caesar. The Sibylline Oracles lists out the emperors (in isopsephy code) multiple times.
Because Revelation 17 specifies not just the number of 'kings', but also when they would told (five have already passed, the sixth is current, the seventh will rule only a short time), it seems the revelator does indeed have specific emperors in mind. On this side, the debate is whether the revelator intended to begin his count with Julius Caesar (as in other apocalyptic literature) or with Augustus (the first 'official' emperor), and whether he intended to skip certain emperors (e.g. Galba, Otho, and Vitellius, who all died within a year after Nero's suicide). Because Revelation 13 seems to depict the death of Nero, yet mentions the beast's unexpected recovery — a true enough summary of the Year of the Four Emperors — he seems to be including the emperor who stabilized Rome, Vespasian.
At minimum, the revelator has in mind Nero, and possibly also Vespasian. Other than that, debate abounds even in critical scholarship.