Jesse and Becky first met in the second episode of Season 2, "Tanner vs. Gibbler".
Jesse and Becky shared their first kiss in season two's "Our Very First Christmas Show" and started dating shortly thereafter.
In "Little Shop of Sweaters", Becky gets Jesse a casual gift to add to his Elvis collection, while Jesse gives her a pair of diamond earrings. He also burns his address book, which causes Becky to tell him that she isn't ready to date him seriously yet, and wants to take their relationship slowly.
Jesse and Becky reveal their love for each other in "Luck Be a Lady (Part 1)" and almost get married in part 2. Becky ends up leaving Jesse at the altar when she realizes their differences, but the two reconcile at the end of the episode and agree to still be a couple.
Jesse and Becky break up a second time in "Breaking Up Is Hard to Do (in 22 Minutes)". They break up because of how they want to spend their time together as a couple, and that Becky wants to go horseback riding and not to the Smash Club and Jesse wants to go to the Smash Club and not horseback riding. However, at the end while Jesse was out with another woman, the woman tells him that he was talking about her all that day. They agree that they love each other and missed each other and get back together.
The pair gets engaged in the Season 4 premiere "Greek Week". While Jesse's relatives visit from Greece, they bring along Silvio, who starts dating D.J., and Eleana (Silvio's older sister) who claims that she and Jesse are married and have been for nearly thirteen years. Becky, upset, finally gets Jesse to explain and Jesse tells Eleana that although she is beautiful, obviously attracted to him and willing to do anything for him, he is madly in love with Becky. This time, although Jesse reminds her that she left him at the alter, Becky says that she will marry Jesse because this time they can plan a real wedding.
Jesse meets Becky's parents in "The Wedding (Part 1)" where Becky's father Kenneth tells him to stop acting irresponsible and that once he's married to Becky, he will have to settle down, literally. After attempting to sky dive with Joey flying the plane, it all goes wrong and Jesse is thrown in the Tomato Country Jail. The two finally marry in part 2.
In "Fuller House", they return from their honeymoon and Jesse moves into Becky's apartment. Michelle is upset by this and soon Jesse and Becky move into the attic of the full house.
Becky goes into labor in "Happy Birthday, Babies (Part 2)" and gives birth to twin boys, Nicholas "Nicky" Katsopolis and Alexander "Alex" Katsopolis.
Becky and Jesse consider moving into their own home in "A House Divided", but soon decide to keep living in the attic.
Becky and Jesse, along with their sons, live in the attic until the final episode, "Michelle Rides Again (Part 2)".
Jesse: "Hi, honey. Are you mad?"
Jesse: "You're so cute when you're mad."