Sheldon and Amy

Sheldon and Amy first met on an online dating site. Although she considers him to be her "kinda-sorta-boyfriend", Sheldon only considers Amy his friend ("She's a girl, she's my friend, she's not my girlfriend"). In more recent episodes, it has been hinted there may be something deeper between them.

As of The Flaming Spittoon Acquisition, Sheldon and Amy are officially classified as "boyfriend/girlfriend".

Their couple name is "Shamy".

Sheldon's Opinion of Amy
Sheldon met Amy when Howard and Raj entered him on an online dating site, but he had to be bribed into meeting her. When he did meet her, he took an immediate liking to her after a brief conversation. In Season 4 they were just texting and emailing, but Penny convinced the pair to start hanging out in person, and eventually go on a date. They began chatting on their webcams, and Sheldon started letting Amy come with them to the Cheesecake Factory and hang out with him at the University.

In the episode The Zazzy Substitution, Sheldon and Amy have a fight over which of their fields is more important, which leads to them breaking up. Sheldon appears to take this change well at first, but later gets 25 cats to try and replace Amy. Leonard calls Sheldon's mother, Mary Cooper, who gets them back together. Sheldon sells all his cats, and he and Amy resume their friendship.

Later on, in The Desperation Emanation, Amy asks Sheldon to meet her mother. Sheldon thinks that Amy wants to take their relationship to the next level, which panics him and he changes his Email Address, his phone number, his mobile number, and his address. Amy however waits for him on the stairs and tells him she isn't wanting to go to the next level. Relieved by this, Sheldon agrees to meet Amy's mother.

When Amy meets Zack in The Alien Parasite Hypothesis she immediently falls in love with him, which Sheldon disapproves of. He gets upset by this and decides to help Amy's urges. He arranges for Amy to meet Zack, but she decides that Zack's stupidity is not worthwhile. While walking home, Amy holds Sheldon's hand, which she calls an experiment. Shortly after, she lets go because she "feels nothing". While holding her hand, Sheldon doesn't mind being her experiment. He also doesn't get angry at her, which is unusual, considering Sheldon's germaphobia.

In the episode The Agreement Dissection, Amy, Penny and Bernadette decide to take Sheldon dancing. Sheldon dances only with Amy, which he doesn't mind. He later follows Amy back to her apartment. They talk for a few minutes before she kisses him on the lips. Instead of getting annoyed Sheldon just says "Facinating."

Sheldon doesn't mind being Amy's experiment and felt jealous when she fell in love with Zack. However he still considers her only as a friend and not a girlfriend, which he points out all the time to the others.

Amy's Opinion of Sheldon
Amy wanted to meet Sheldon when they met on a dating site. She immediately liked him.

In the episode The Desperation Emanation Amy tries to convince Sheldon to meet her Mother which worries Sheldon. When he gets the wrong idea she goes to clear it up by telling him it's just to please her Mother.

When Amy first meets Zack in The Alien Parasite Hypothesis she instantly gets a crush on him. When she and Sheldon try to find out why she acted oddly when she met him she decides to face the truth while Sheldon refuses to which makes her suspect him of feeling jealous of Zack. Sheldon arranges Amy to meet Zack and she tells Zack how she feels about him but when she sees how stupid he is she changes her mind like Penny did. After she and Sheldon left she holds Sheldon's hand telling him it's an experiment but takes her hand away saying, "no, nothing. Never mind."

Later in The Agreement Dissection the girls,except Priya, takes Sheldon to a bar where they question Sheldon about him kissing girls. Sheldon tells them he has never kissed a girl and Amy tells him she's "open for experimentation" and tries to kiss him but he refuses. Later in the episode she and Sheldon dance together before she takes him to her apartment. In her apartment she gives him advice about dealing with Priya. She then kisses him before throwing up in her bathroom.

Amy thinks Sheldon as her boyfriend and is willing to kiss him and offer him advice.

The Differences between Sheldon and Amy
While Amy is dubbed the female version of Sheldon, her appearances on the show have given audience the chance to get to know her better and realize that Amy is not exactly a Sheldon clone, though she may be perhaps the closest version of Sheldon that could ever be found. Here are some of the notable differences between the two:
 * Sheldon adores Star Trek and everything it contains, such as Spock, the actors involved such as Leonard Nimoy and Wil Wheaton, he even speaks fluent Klingon, a language originating from the franchise. Amy however views Star Trek as a cheap science fiction.
 * Sheldon does not drink and is not willing to compromise that. Amy, despite initially not a drinker, changes afterwards to become a casual drinker, especially after hanging out with Penny and Bernadette. In the Isolation Permutation, a drunk Amy told Sheldon and Leonard that she came to the liquor store to get a bottle of wine "like Penny taught me to do when you're sad".
 * Amy can play the harp and seems to enjoy playing the harp as a way to let loose. This can be shown when she played the Girl from Ipanema and REM's Everybody Hurts, to represent her sadness at being left out from bridesmaid dress shopping by Penny and Bernadette. Sheldon however, cannot stand harp music, stating that it reminds him of a painful past experience.
 * Sheldon's major branch of science is in Physics while Amy's major branch of science is in Biology.
 * Sheldon loves train and in Season 5's The Pulled Groin Extrapolation started playing with toy train. Amy meanwhile has never shown any slight interest in toy train whatsoever.
 * Sheldon had a fear of birds, or Ornitophobia but Amy has never had Ornitophobia.
 * According to Bill Prady, one of the co-writers of the show, at the Comic Con 2011, while both Amy and Sheldon missed out a lot growing up, Sheldon does not mind it but Amy does.
 * Though Sheldon and Amy can both be too straightforward in their words as if they have no filter, Amy phrases herself better than Sheldon, even though she is just as awkward. In "The Rhinitis Revelation", Sheldon used the term "stupid person" while Amy used the term "the less intelligent".