Revelation 12:9, “And the great dragon was thrown out, the ancient serpent, the one called the Devil and Satan, who deceives the whole world, he was thrown to the ground, and his angels were thrown out with him” (emphasis mine).
Revelation 12:11 explains that Satan’s being cast out of heaven relates to the conquest that came by the blood of the Lamb, Christ’s death on the cross. Revelation 12:10 explains that “the one who accuses the brothers” is the one who has been cast out. It seems, then, that the result of Satan being “cast out” in Revelation 12:9 is that his accusations against believers are rejected because of the blood of the Lamb.
Having been cast out, Satan’s time is short (Rev 12:12), and he uses that time to make war on the rest of the woman’s seed (i.e., believers) and to deceive the nations (13:3-8). Satan gives his authority to the beast (13:3), the beast exercises authority for forty-two months (13:5), “and authority was given it over every tribe and people and language and nation” (13:7). Satan’s deceptive power in the beast is so strong that it persuades everyone except the elect (13:8).
Revelation 20:1-3 says that there will be a thousand year period in which he no longer deceives the nations.