A piano version of "Great Gate of Kiev" is played in the background as the gag showcases artwork of each Simpson. The camera turns to the Simpsons sitting at an art gallery. Homer grabs the remote control and all the artwork on the wall changes channels, pleasing the family.
The Simpsons go to Diz-Nee-Land where the lines for the rides are terrible, except for this one rocket called "Rocket to Your Doom" that takes them to the home planet of Kang and Kodos, Rigel VII where the inhabitants try to eat Homer in a giant fondue.
The Simpsons go to Diz-Nee-Land. After a really long journey, they dislike all of the lame games and rides they visit, and decide to go to "Journey to your Doom", a just-opened ride which isn't on the map.
They get in, and it immediately transforms into a space ship. At first, the family is skeptical, but a screen appears, and Kang and Kodos tell them that they are being taken to Rigel 7.
At the planet, Kang and Kodos show them around on a giant pet cage, and the Simpsons are informed they are prisoners. Then they are taken as exhibitions to a Zoo, and after a while, they are informed they must choose one of them to be dined in a ritual. Everybody votes for Homer; even he changes his vote from Bart to himself after seeing the other votes.
After, we can see Homer walking in something that looks like a bacon underwear, to be eaten; but he gets rescued by some hippie-looking Rigelians who believe that eating other sentient species is wrong. After an excessive party, he gets on another space ship, only for one, that also pleases all desires, but he realizes he wont enjoy it without his family and goes back to rescue them.
The Rigelians, in the mean time, have decided to eat the rest of the family, and they are glazed over giant plates with some lettuce and tomato. When Homer offers to be eaten instead, he gets put on a similar plate, and bothers the cook by eaten the glaze and claiming he didn't got any.
The Rigelian queen then eats Homer's previously off-camera severed buttock and gets poisoned because of the fast food life they all eat; even Lisa is the worst polluted of them all. The queen dies, and the Simpsons get sent home, on a space ship that looks like the interior of the original starship Enterprise. They set course to Earth, but after a call from Abe, the family decides to go everywhere else. Then, the credits happen over a montage of several images spoofing Star Trek TV and movie scenes.
The episode was originally scheduled to air on May 19, 2013 as the finale of Season 24, but was replaced by "Dangers on a Train".  As a result, the production code is much older than the rest of Season 26.