Sometime after the events of the first Planet of the Apes, the climax of which is repeated frame for frame at the beginning of this sequel, another set of astronauts arrives on the far-future Earth that is the titular planet.
This time it's Brent (James Franciscus) who survives the crash landing and learns that evolved simians have taken over the world, post-apocalypse. After hooking up with Nova (Linda Harrison), the mute, fur bikini-clad beauty who spent the first film being squired by astronaut Taylor (Charlton Heston), Brent confers with Zira (Kim Hunter) and Cornelius (David Watson, giving Roddy McDowall his only break during the five-film series), the ape scientists whose adherence to scientific principles makes them friendly to the possibility of intelligent human life.
Something of a military coup has taken place among the apes, who dispatch an army to the desolate Forbidden Zone where Taylor has coincidentally disappeared.
With the apes and the humans both rooting about in the ruins of 20th century civilization, it's only a matter of time before they all find out what happened to the other survivors of the nuclear holocaust.