The Enterprise take on six passengers of the stolen space cruiser, Aurora, after they are forced to destroy it before it enters Romulan-controlled space. The six passengers are "space hippies" led by Dr. Sevrin, who want to live free on the mythical planet of Eden. Spock sympathizes with them and helps find the planet, but Dr. Sevrin has his own plans to get there.

In the 21st century, all travel is conducted via T-Mat, an instantaneous travel and transport system operated from a Moonbase. Space flight has been all but forgotten - and as a result, when contact is lost with the Moonbase, there appears to be no way to repair T-Mat system. As the world begins to slide into chaos and anarchy, the Doctor and his companions arrive just in time to volunteer for an emergency rocket flight to the Moon, where they discover that the Moonbase has been invaded by Ice Warriors. Now T-Mat is under their control, and despite resistance from the Moonbase crew, the Ice Warriors will soon be able to use it as a weapon to transmat deadly seed pods to Earth, transforming the planet's atmosphere and climate and enabling their army to invade.