Moss debuted at the age of 6 with the miniseries Lucky Chances. She played the kid who was primarily focused on dancing rather than acting. Moss went to New York in order to attend the School of American Ballet and then shifted to study at Kennedy Center, along with Suzanne Farrell.
She also played Baby Louise in the film adaptation of the Broadway play, Gypsy. At the age of 16, she landed a role in Girl, Interrupted, alongside Angelina Jolie. She was very convincing with her role as a teenage burnt victim and got praised for her performance.
Around the same time, she landed another position on the TV series, The West Wing. Moss appeared on Mad Men, which is her most acclaimed role to date. Moss played Peggy Olson, who demands equality with the male characters in the story. The role earned her various nominations, including Emmy and Golden Globe.
She also made her Broadway debut with speed-the-Plow. Apart from that, she has also worked on Top of the Lake, The One I Love, Listen Up Philip, The Heidi Chronicles, Truth, Queen of Earth, The Handmaid’s Tale, Her Smell, Us, and The Invisible Man. Moss married Fred Armisen in 2009, and the couple is apparently still together.