Dimension C-137 first appears in the "Pilot" episode and appears in every episode after then until "Rick Potion #9", wherein it makes its last appearance until season 3. In "Rick Potion No. 9", Rick makes a love potion using vole DNA for Morty to use on Jessica. However, the side affects of the potion leads to a disaster. The chemicals in the potion piggyback on the flu virus, causing everyone in Morty's school to fall in love with him.
To counteract this, Rick mixes praying mantis DNA with a more contagious strain of the flu virus. Unfortunately, this backfires, turning not only those affected by the original potion into praying mantis monsters set on mating with Morty, but the entire world (presumably due to the aggressive nature of the flu strain Rick used) into praying mantis creatures that want to mate with Morty, then kill him afterwards. Rick uses an antidote on them, but this again backfires, turning all of humanity into deformed, disgusting monsters known as Cronenbergs (except for Jerry, Beth and Summer). Unable to solve this increasingly difficult problem, Rick seeks out a different reality where he manages to restore humanity to normal. There, that dimension's version of Rick and Morty have recently died, so Dimension C-137's Rick and Morty take their places without anyone noticing.
Meanwhile, alternate versions of Rick and Morty from yet another dimension where everyone is born a Cronenberg, named Cronenberg Rick and Cronenberg Morty, do exactly the same thing in their dimension and turn everyone into normal humans. They leave their own dimension and enter Dimension C-137, where every normal human is now a perfect Cronenberg matching their home dimension.
As of now, Dimension C-137 is completely overrun by the Cronenberg species and the only three known humans are Jerry, Beth and Summer who are living out the rest of their lives in a post-apocalyptic world, where they survive by hunting and eating the Cronenbergs. Jerry and Beth are now happy with each other in their relationship. They take turns with Summer acting out movies from memory to make up for their lack of entertainment. At the end of Rick Potion #9, Summer can be seen acting out a scene from Jaws. Beth also mentions that she has finally achieved true happiness now that her father Rick and her son Morty are no longer with her.
The Cronenberg species and the rest of the Smith family are apparently far apart enough, that they never interact with each other, for unknown reasons, so both species don't need to worry about each other and the Cronenberg versions of Rick and Morty never have to interact with the Smith family.
Dimension C-137 is mentioned again in the episode "Rixty Minutes", when Morty shows Summer the graves in the backyard where Rick and Morty are buried, telling her the whole story of Rick Potion #9. It is also mentioned again in "Close Rick-Counters of the Rick Kind", by the Council of Ricks and it is also briefly seen in a screen, showing Rick's memories. The memories include Rick putting the helmet on Snuffles from the episode "Lawnmower Dog", Rick holding Morty when he is an infant, and Rick giving the love potion to Morty from "Rick Potion #9". There are also scenes of Rick and Morty flying in the space cruiser, and one of Rick, lying down on the floor, and Morty passing him his canister, but it is unknown if these take place in the old or new dimension. In the episode "Total Rickall", there is a flashback montage to all the funny catch phrases that Rick has used. One of which is one he was using, while playing cards with Snuffles. This has to be Dimension C-137, because Snuffles leaves the family in the episode "Lawnmower Dog", before events of the dimension transition in the episode "Rick Potion #9". There are many other flashbacks of moments in time that actually happened, but none of them prove that they occur in Dimension C-137.
Dimension C-137 is briefly mentioned in the episode "Mortynight Run", when Rick is asked to identify his home dimension for identification purposes when returning to pick up his Jerry. Because Jerry is not from Rick and Morty's home dimension of C-137, Rick marks him as "N/A". This might mean that Rick is uncertain of their current dimension's official alphanumeric identification.
Dimension C-137 returns in the episode The Rickshank Rickdemption, Morty brings the Summer from the new Dimension he and Rick came from in order to show her that Rick doesn't care about anyone and that he always leaves carnage in his wake. It is here, Summer meets the version of herself and her family from this Dimension, who are now more tribal and savage than when they were previously seen.
The comic Rick and Morty Issue 45 is set entirely in the Cronenberged C-137 world. Summer is growing increasingly sad, realizing that eventually her parents will die, leaving her entirely alone. Cronenberg-Morty then seeks her out, however, explaining that Cronenberg-Rick has become totally unhinged and evil - due to living with nothing but the other Cronenbergs, which from their perspective are just feral animals. Cronenberg-Rick has assembled a group of the most evil Ricks in the multiverse at his lair in the local observatory, to conduct a magic ritual to summon the absolute worst Rick, "Old God Rick" (a Cthulhu-like demon), who will destroy the entire multiverse.
Cronenberg-Morty managed to locate the Space Cruiser that this universe's Rick and Morty left behind on a rooftop in the city (Summer and her family hadn't found it because they avoided the denser concentration of monsters there). Jerry arrives at the last minute to help them fight through to the ship. Cronenberg-Morty intends to use the Neutrino Bomb in the space cruiser to destroy the evil Ricks before they can finish their ritual (which has apparently been depowered or deteriorated to the point that it will blow up the observatory, but not the entire planet). Morty explains that the ship won't recognize him as a pilot due to being a Cronenberg himself, so he needed to seek out one of them to do it. Summer knocks out Jerry so she can make a suicide run with the ship, explaining as she leaves that she realized she has no future in Cronenberg world, doesn't want to be totally alone there after her parents are gone, and this is her chance to be a hero for them. Jerry and Cronenberg-Morty witness the bomb detonating in the distance, killing the evil Ricks and (presumably) Summer. Jerry then heads back home with Cronenberg-Morty, saying his mother is waiting for him (implying Jerry intends to eat Cronenberg-Morty).
The events of the comic may not be canon. Not only is not totally confirmed if Summer is dead, there are several mismatches between it and events in the TV series. In the comic, original-Summer openly wonders what happened to her Rick and Morty, and at first, is worried that they got turned into Cronenbergs just like everyone else: Cronenberg-Morty has to explain to her that the Rick and Morty of this dimension abandoned it for another one. Granted, original-Jerry correctly assumes that Rick and Morty just fled to another dimension, but Summer refuses to believe this is true. However, this comic is based on the appearance of Cronenberg World when it reappeared in Season 3: when original Summer met original-Morty and the new Summer.
- "Lawnmower Dog"
- "Anatomy Park"
- "M. Night Shaym-Aliens!" (cameo)
- "Meeseeks and Destroy"
- "Rick Potion #9"
- "Rixty Minutes" (mentioned)
- "Close Rick-Counters of the Rick Kind" (cameo; Morty also says "my name is Morty Smith from Earth Dimension C-137")