In the third-season finale, Raj and Howard sign Sheldon up for online dating to find a woman compatible with Sheldon and discover neurobiologist Amy Farrah Fowler. Like him, she has a history of social ineptitude and participates in online dating only to fulfill an agreement with her mother. This spawns a storyline in which Sheldon and Amy communicate daily while insisting to Leonard and Penny that they are not romantically involved. In "The Agreement Dissection", Sheldon and Amy talk in her apartment after a night of dancing and she kisses him on the lips. Instead of getting annoyed, Sheldon says "fascinating" and later asks Amy to be his girlfriend in "The Flaming Spittoon Acquisition". The same night he draws up "The Relationship Agreement" to verify the ground rules of him as her boyfriend and vice versa (similar to his "Roommate Agreement" with Leonard). Amy agrees but later regrets not having had a lawyer read through it.
After Sheldon has a food truck moved away from the building, Leonard and Penny are shocked to find he is the leader and sole member of the Tenants' Association for the building. Amy doesn't want to be caught in the middle but secretly suggests they rally support from the other tenants to vote Sheldon out. Nobody else supports Leonard so Amy tells them Sheldon was never added to the lease when he moved across the hall with her. Sheldon fires back with his own legal technicality so Amy is forced to support Leonard. She makes Sheldon happy by saying he can be Leonard's official opposition, making Leonard believe he made a mistake. Meanwhile, Howard and Raj find a drone. Raj returns it to the cute owner Cynthia and gets her number. Unfortunately, Cynthia watches footage of Raj on the drone and is immediately turned off.
"Big Bang" thrived with the addition of new characters, including scientists Amy (Bialik) and Bernadette (Rauch) and comic-book-store owner Stuart (Kevin Sussman), says Helberg, part of the original cast with Galecki, Parsons, Cuoco and Nayyar. (The show eventually spawned a hit prequel spinoff, "Young Sheldon," which heads into its third season in the fall, most likely in the "Big Bang" time slot.)
Star Trek in particular is frequently referenced and Sheldon identifies strongly with the character of Spock, so much so that when he is given a used napkin signed by Leonard Nimoy as a Christmas gift from Penny he is overwhelmed with excitement and gratitude ("I possess the DNA of Leonard Nimoy?!"). Star Trek: The Original Series cast member George Takei has made a cameo, and Leonard Nimoy made a cameo as the voice of Sheldon's vintage Mr. Spock action figure (both cameos were in dream sequences). Star Trek: The Next Generation cast members Brent Spiner and LeVar Burton have had cameos as themselves, while Wil Wheaton has a recurring role as a fictionalized version of himself. Leonard and Sheldon have had conversations in the Klingon language.
On October 9, 2007, a full-length (1 minute and 45 seconds) version of the song was released commercially. Although some unofficial pages identify the song title as "History of Everything," the cover art for the single identifies the title as "Big Bang Theory Theme." A music video also was released via special features on The Complete Fourth Season DVD and Blu-ray set. The theme was included on the band's greatest hits album, Hits from Yesterday & the Day Before, released on September 27, 2011. In September 2015, TMZ uncovered court documents showing that Steven Page sued former bandmate Robertson over the song, alleging that he was promised 20% of the proceeds, but that Robertson has kept that money entirely for himself.
Sheldon and Amy are surprised to find that Wil Wheaton's new Professor Proton show is actually very entertaining and that Wil had Howard on as a guest. On Howard's suggestion, Sheldon apologizes to Wil, mending their friendship, and tells him he wants to be on the show; but Wil asks for Amy. Sheldon tells her to do it, but she says she often doesn't do things to avoid upsetting him. Sheldon is horrified when he realises how selfish he has been, especially when he finds out that the men do the same for him. Sheldon encourages Amy to go on the show to inspire girls to pursue science while trying to control his obvious jealousy for her. Meanwhile, Leonard writes a book about a physicist that solves a murder, the protagonist Logan Dean is based on himself. Bernadette points out Logan's mean boss Illsa is similar to Penny, who thinks it is based on Bernadette, though Leonard does not correct her. However, Bernadette tells Penny the truth, upsetting her and making her mad at Leonard. After calling his mother for advice, Leonard learns that Illsa is actually like her; but abandons the book when he realizes he wrote romantic tension into the relationship between the characters.