When Jesus returns, He will throw the beast and the false prophet alive into the Lake of Fire.
Revelation 19:20 (NKJV)
20 Then the beast was captured, and with him the false prophet who worked signs in his presence, by which he deceived those who received the mark of the beast and those who worshiped his image. These two were cast alive into the lake of fire burning with brimstone.
The devil, or Satan, is meanwhile shut up for a thousand years.
Revelation 20:1–3 (NKJV)
20 Then I saw an angel coming down from heaven, having the key to the bottomless pit and a great chain in his hand. 2 He laid hold of the dragon, that serpent of old, who is the Devil and Satan, and bound him for a thousand years; 3 and he cast him into the bottomless pit, and shut him up, and set a seal on him, so that he should deceive the nations no more till the thousand years were finished. But after these things he must be released for a little while.
When the thousand years are ended, he will be released for a little while, and he will deceive the nations, inspiring a rebellion. Afterwards...
Revelation 20:10 (NKJV)
10 The devil, who deceived them, was cast into the lake of fire and brimstone where the beast and the false prophet are. And they will be tormented day and night forever and ever.
The beast and the false prophet will have already been in the Lake of Fire for more than 1,000 years when the devil goes there, yet it is where they are (present tense). If they did not exist (if they had been burned up), it would make more sense for them to be referred to in the past tense ("were"). Now, since the beast and the false prophet have not burned up after 1,000 years, how long would they have to wait until they cease to exist?
They will be tormented day and night forever and ever.