Plaza graduated from Ursuline Academy, an all-girls Catholic school, in 2002. In high school she was student council president and participated in productions with the Wilmington Drama League. She studied film at New York University’s Tisch School of the Arts, graduating in 2006.

On March 12, 2010, Plaza performed at “A Night of 140 Tweets: A Celebrity Tweetathon for Haiti”, produced by Rob Huebel, Paul Scheer, Ben Stiller, and Mike Rosenstein, at the Upright Citizens Brigade Theatre in Los Angeles.

In 2011 she appeared on Portlandia. Plaza appeared as a guest judge during a roast segment on The Next Food Network Star in 2011. She appeared in Episode 199 of the WTF with Marc Maron podcast. She also had a recurring role as “the Princess” in the comedic sci-fi web series Troopers on CollegeHumor.

In 2012, she was featured in Father John Misty’s music video for the song “Hollywood Forever Cemetery Sings” from the album Fear Fun and in 2014 she was in Cassorla’s “Bona Fide” video where she also made her saxophone-playing debut.

In 2012, Plaza earned her first starring role in a major film, alongside Mark Duplass, in the comedy, Safety Not Guaranteed. Plaza played Darius, a jaded intern who answers a curious want ad “seeking a companion for a time traveling adventure”. Her performance in the film was critically acclaimed, and Gary Thompson of The Philadelphia Inquirer questioned whether this role was out of her usual “pretty slacker” range but found her performance “compelling”.

In 2013, she had the leading female role as Sacagawea in Drunk History episode Nashville in the segment on Lewis and Clark Expedition.

At the 2014 Sundance Film Festival in January 2014, Plaza’s film, Life After Beth, which was written and directed by her boyfriend Jeff Baena, premiered. Plaza also voiced Grumpy Cat in the Lifetime Network’s original movie Grumpy Cat’s Worst Christmas Ever (2014).

She starred in Mike and Dave Need Wedding Dates alongside Zac Efron, Anna Kendrick and Adam DeVine. The film was released on July 8, 2016. Her role as the rebellious Tatiana earned her critical praise.

In 2016, she was a guest star on HarmonQuest, as a gnome named “Hawaiian Coffee” and portrayed Aaron Burr in the “Hamilton” episode of Drunk History.

Plaza dated actor John Gallagher Jr. when they were both 15 years old. In 2016, Plaza said that she used to be in a relationship with actor Michael Cera. Plaza has been in a long-term relationship with writer and director Jeff Baena since 2011. They live together in Los Angeles, California, and work together often.

In 2016, Plaza mentioned in an interview to The Advocate that: “I know I have an androgynous thing going on, and there’s something masculine about my energy. Girls are into me — that’s no secret. Hey, I’m into them too. I fall in love with girls and guys. I can’t help it.”

In 2017, Plaza both starred in and produced two films, The Little Hours and Ingrid Goes West. It was announced that she would star in indie comedy An Evening With Beverly Luff Linn in 2018.

Plaza starred as both Amahl Farouk / Shadow King and Lenny Busker in the FX series Legion from 2017 to 2019. On February 23, 2019, Plaza hosted the 34th Independent Spirit Awards.

In 2019, she starred in Child’s Play, a reboot of the 1988 film, as Karen Barclay, Andy’s mother who brings home a killer doll, Chucky.

In February 2020, Plaza starred alongside Bill Murray in a short parody of Robert Eggers’ The Lighthouse in order to promote the upcoming Independent Spirit Awards.