Moss also played Zoey Bartlet, youngest daughter of President Jed Bartlet in The West Wing, and is set to star in the upcoming BBC mini-series Top of the Lake.
Today (July 24), Moss celebrates her 30th birthday, and to celebrate we've rounded up ten fast facts about her.
1. Born in Los Angeles, California on July 24, 1982, both of Elisabeth Singleton Moss's parents were performers. Her English father Ron was a jazz musician and manager, and her mother Linda, played the harmonica.
2. Moss was home-schooled and worked hard, describing herself as "serious" and "focused". Her favourite thing to do as a child was play 'Library', where she would stack books on the floor and check them out to her parents, a game that combined her love for learning with her love for performing.
3. As a child, Elisabeth studied dance with famed ballerina Suzanne Farrell in Washington DC, while auditioning for and appearing in various films and TV shows. After landing a role in Girl, Interrupted, Moss decided to fully commit to acting.
4. In Girl, Interrupted Moss played burn victim Polly. She followed it up with a string of roles in film and television, including a recurring role in The West Wing from 1999 to 2006, as Zoey Bartlet. She also had small roles in Grey's Anatomy and Heart of America.
5. Since 2007, Moss has played Peggy Olson in Mad Men. She has been nominated for three Emmys for the role, twice for 'Outstanding Lead Actress in a Drama Series' and once for 'Outstanding Supporting Actress'. She has lost out all three times, but has been nominated again for 'Outstanding Lead Actress' in 2012.
6. Moss met Saturday Night Live star Fred Armisen after appearing on an episode of the show hosted by Mad Men co-star Jon Hamm. They married in October 2009, separated eight months later, and divorced in May 2011.
7. Elisabeth also works on the stage and made her Broadway debut in October 2008 in Speed-The-Plow opposite Jeremy Piven and William H. Macy. In January 2011 she made her West End début in The Children's Hour. She met Keira Knightley while performing in the play, and the two are now good friends.
8. Moss's parents introduced her to Scientology at a young age and she has been a devout follower ever since. Elisabeth studied at The Learning Connection, an acting school run by the church. She says of the religion: "It's one thing that has helped me at times, and it's kind of as simple as that."
9. Elisabeth starred in the sci-fi drama Invasion in 2007. She was originally only going to appear in one episode for a guest appearance, but did such a good job that she was added to the cast and went on to appear in multiple episodes of the show.
10. Moss is afraid of heights, spiders and deep water.
Mad Men Season Five - photo gallery