She played President Jed Bartlett's daughter Zoe on The West Wing and Peggy, the strong-minded copywriter on Mad Men.
And this year Elisabeth Moss stars in two high-profile TV series that will almost certainly lead to her picking up more acting awards.
Moss is Offred in The Handmaid's Tale based on Margaret Atwood's story of fertile women being forced to bear children for elite couples in a future totalitarian USA.
And she returns as troubled Kiwi police detective Robin Griffin in the second series of Jane Campion's psychological crime thriller Top of the Lake.
Robin Griffin has a difficult past that's catching up with her despite her move to a new beat in Australia.
Nicole Kidman, the statuesque Gwendoline Christie from Game of Thrones, and Jane Campion's daughter Alice Englert are among the actors joining the cast of Top of the Lake: China Girl.
While the first series was filmed in New Zealand, number two is shot around Bondi Beach in Australia and is set five years later.
Moss says she had wondered what had happened to Robin after the punishing climax to the first story.
“I thought she would not be in a great place at the beginning of China Girl, and of course Jane and Gerrard [Lee] took it much further and put her in a terrible place.
“The first season was so much about her trying to find Tui in this wilderness and having to confront this landscape she had run away from, and now she’s slap-dab in the middle of this urban area. She can’t hide and she can’t run.”
The tide has turned for female actors, Moss says.
“There are so many television shows that are run by women and are led by a woman. The people that hold the purse strings, that finance these projects, finally woke up and realised this is what we want to see and these projects make money.”
Campion’s gift for exploring the dark side resonates with many of us, Moss says.
“It’s unexplored territory, you’re addressing things people don’t want to look at. People run away from the dark underbelly of various places and worlds. It’s something we don’t often get to see.”
The Handmaid’s Tale brought Moss and the writers who adapted Margaret Atwood’s 1985 novel critical plaudits.
Moss credits MGM and Hulu for seeing possibilities in the novel, and the skill of the writers in adapting it.
“I connected to the idea of a woman who had lost everything and who, more importantly, wasn’t giving up. I think that’s a very relevant idea.”