She is best known for her starring role as Martha Hanson on the FX period spy drama series The Americans (2013–2017), for which she received critical acclaim and a Primetime Emmy Award nomination in 2017.
From 2015 to 2019, Wright starred as Marjorie in the Amazon Prime Video crime drama series Sneaky Pete, receiving positive reviews.
[4] In 2018, she had a starring role as Ada in the historical drama film Ask for Jane and as Emilia in a stage production of the Shakespearean tragedy play Othello at Delacorte Theater.
[11] In 2020, Wright began a starring role in the TNT post-apocalyptic dystopian thriller series Snowpiercer (2020–2022), based on the 2013 film of the same name by Bong Joon-ho.
[12] Also that year, she made a guest appearance as Ms. Roswell, the gatekeeper to Ace Studios, in the Netflix period drama miniseries Hollywood.