Thirteen, played by Olivia Wilde, is introduced as part of the new diagnostic team in season 4 of House. She is intensely private, and initially doesn't even share her name with her potential co-workers, hence the name Thirteen.
Over time, House comes to respect her as a talented doctor, and the two build a relationship of mutual trust and understanding of each other's personalities. Wilson later states that House is better with her on his team, saying "He needs someone who doesn't need him. You're the only one he's never really been able to suck into his crazy House vortex. Keeps him grounded, his ego in check."
Her sexuality is alluded to a few times. In "Don't Ever Change" (S4E12), House and Foreman both assume that she is bi, but she doesn't confirm it. In season 5, her sexuality is confirmed and she ends the series in a committed relationship with her girlfriend, Amy.