Amy makes her debut in the third season finale titled "The Lunar Excitation". In the episode, Raj Koothrappali (Kunal Nayyar) and Howard Wolowitz (Simon Helberg) find Amy through an online dating site, after establishing an account with Sheldon's name and information. The site matches her with Sheldon Cooper, since the two share many similar traits. Upon meeting, Amy and Sheldon become acquainted. The two initially communicate via text messages and video calls and eventually begin meeting in person.
Early on, Amy is shown as coldly rational, displaying little emotion, and appears awkward in social situations. She is initially ambivalent and often condescending towards Penny (Kaley Cuoco) and Bernadette Rostenkowski (Melissa Rauch). As they grow closer, she sheds her strident, aloof personality for a more feminine and social one, although retaining some social awkwardness. Amy begins to consider Penny a close friend, sometimes referring to her as her "bestie", and occasionally admitting that her entire social life revolves around Penny. Amy also often demonstrates an infatuation towards Penny, occasionally bordering on physical attraction. Amy tends to display a condescending attitude towards Bernadette, although she still considers her a close friend. Her feelings towards Sheldon grow considerably over time. Amy considers him to be ideal in almost every way, though sometimes she displays frustration with Sheldon's quirks, and his refusal of physical intimacy.
In season 5, after Amy goes out on a date with comic-bookstore owner Stuart Bloom (Kevin Sussman), Sheldon decides to solidify their relationship as boyfriend/girlfriend with a 31-page "Relationship Agreement". Later in the season, Amy begins a campaign to increase Sheldon's feelings for her by becoming more involved in his interests, including video games and Star Trek.
By the beginning of season 6, Sheldon and Amy regularly display signs of affection, such as holding hands, although Amy wants the relationship to evolve further to include sexual intimacy. By mid-season, Sheldon gets some intimate views of Amy when he cares for her while she has the flu. She also provides Sheldon with consoling hugs. On one Thanksgiving, Amy receives a slap on the rear by an intoxicated Sheldon who tells everyone that she is a "great gal."
In the season 7 episode "The Locomotive Manipulation", Amy wants to have a romantic Valentine's night with Sheldon and arranges for them (along with Howard and Bernadette) to have dinner on a train. While on the train, they meet Eric, another train enthusiast who engages Sheldon in conversation during dinner. Amy is upset about it, first sparking Bernadette, then Amy herself to confront Sheldon. Sarcastically, Sheldon says he will give Amy the romance she wants. He openly mocks her, staring into her eyes and then kissing her. At first, the kiss is forced, but then he leans in and appears to enjoy it.