In "An Indirect Kiss", Connie says to Steven "You don't need to have powers to be here with me" and almost kisses Steven, but she feels something, realising that she can see without her glasses.
In "Sworn To The Sword", Connie goes through a tiring, almost dehumanising process to protect Steven. At the end of the episode, they decide to fight with each other instead of one protecting the other. They are extremely good at working together and they called themselves 'jam buds', both in the beginning and the end at the episode.
Connie and Steven dance together in "Alone Together" and fuse into Stevonnie. They spend the rest of the episode having fun as Stevonnie, but they eventually realise that they have just as much fun as separate people as well.
In "Steven's Birthday", Garnet and Pearl play romantic music for together and Steven and Connie dance. After Steven is restored to normal, Connie tells Steven that she likes him just the way he is. When Steven sacrifices himself and fakes his death in "I Am My Mom", he says "I love you" to Connie.
In "Beach City Drift", Steven is mad at Kevin while Connie is calm. This might be a parallel to Ruby and Sapphire, as both ships are in a romantic relationship.
In "Open Book", Steven and Connie discuss the ending to her favourite book series. While Connie wishes the ending were different, Steven doesn't. However, he hides this fact and agrees with Connie in an attempt to impress her. Later in the episode, in Rose's Room, a fake version of Connie materialises in a wedding dress. The fake Connie traps Steven until he admits he likes the ending, and the real Connie says that she cares more about Steven than a book.
In "Escapism" and "Change Your Mind" Connie and Steven work together to convince the Diamonds to free Homeworld from their tyranny. They fuse into Stevonnie at the Era 3 ball, and are consequentially punished by Blue Diamond for doing so. However, the two persuade Blue Diamond to let them go, and they confront the other Diamonds together.
In "Steven Universe: The Movie", Connie gives Steven a peck on the cheek before heading off to space camp, and Steven blushes, indicating they they indeed have romantic feelings for each other.
After the movie, Steven expresses his fear that Connie is leaving him behind for a more normal life. He begins to feel insecure about Connie's human friends in "Bismuth Casual". When he tells her this, Connie assures Steven that they'll always care for each other, and they fuse into Stevonnie.
In "Together Forever", Steven realizes that he wants Connie to be his future and is encouraged by Ruby and Sapphire to propose to her and become their fusion Stevonnie permanently. However, when he proposes, Connie becomes concerned and responds with a gentle rejection and a "not now". Despite the reassurance that she might want to be with him someday in the future, Steven is still completely crushed.
Steven begins to start swelling due to his stress and trauma in "Growing Pains", and he visits Dr. Maheswaran to try to control it. He begins to swell bigger when he is reminded of Connie's rejection, signifying that Connie means a lot to Steven. Connie also shows concern for him in this episode.
In "I Am My Monster", Steven transforms into a monster under the weight of his own burdens and terrible perceptions of himself. When the Diamonds respond to this by blaming themselves dramatically, Connie appears on Lion and confirms that while it is indeed the Diamonds' (and to an extent Spinel's) fault, blaming themselves won't help Steven.
While the other Crystal Gems hug him in this form and reassure him that they still love him, Connie comes up to him the last. She proceeds to kiss him, and this is the final act that turns Steven back to normal, showing that Connie is one of the most important people in Steven's life, if not the most important, and that he cares about her a lot.
In "The Future", as Steven says goodbye to everyone as he gets ready to leave Beach City, he and Connie are presumably in a romantic relationship, as they kiss and already have plans to meet up again soon.
- “Steven... you must have been so afraid to show us this side of yourself. But we're not going anywhere. We're all gonna take care of you the same way you take care of us. You know what? I don't have your powers, but...”
- — Connie
The ship generally doesn't receive much controversy as its cute and the interactions are healthy. There are some people however, who would prefer them as friends.
On AO3, Connverse is the most written ship for both Steven and Connie. It's also the fifth most written ship in the Steven Universe (Cartoon) tag.
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