Moss began acting in the early 1990s and first gained recognition for playing Zoey Bartlet, the youngest daughter of President Josiah Bartlet, in the NBC political drama series "The West Wing" (1999–2006). Wider recognition came for playing Peggy Olson, a secretary-turned-copywriter, in the AMC period drama series "Mad Men" (2007–2015). She won the Golden Globe Award for Best Actress – Miniseries or Television Film for portraying Detective Robin Griffin in the BBC miniseries "Top of the Lake" (2013), and she won the Primetime Emmy Award for Outstanding Lead Actress in a Drama Series and Outstanding Drama Series for producing and starring as June Osborne in the Hulu dystopian drama series "The Handmaid's Tale" (2017–present).