2011–2019: Mature roles and critical recognition
In 2011, she starred alongside Freddie Highmore in the romantic comedy The Art of Getting By. She also played the role of Jill Roberts in the Wes Craven film Scream 4. Roberts next appeared in the 2012 film Celeste and Jesse Forever, parodying pop stars such as Kesha with her performance as Riley Banks, an incurious blonde singer. Roberts said in an interview that her role as Banks tempted her to write an album of songs using her character as an alter ego. On February 7, 2013, The Hollywood Reporter confirmed that Roberts had been cast to star in a pilot for Fox called Delirium, based on the Lauren Oliver novels. She portrayed Lena Haloway, the protagonist, but Fox decided not to pick up the show. The pilot episode was picked up by Hulu and was available to stream for a limited time beginning on June 20, 2014.
Roberts co-starred with John Cusack and Evan Peters in the comedy-drama film Adult World, released on April 18, 2013. Roberts played a recent college graduate who works at a sex shop to make ends meet. She has said that most of her lines were ad-libbed so her reactions in the film were completely genuine. Her performance was praised by both Andrew O'Hehir of Salon and Stephanie Zacharek of The Village Voice, who praised Roberts' performance as "both breezy and carefully tuned". In the next month, she guest starred as Amanda Barrington in the animated sitcom Family Guy, in the episode "No Country Club for Old Men". Roberts then starred in the comedy film We're the Millers, alongside Jennifer Aniston and Jason Sudeikis. It was released on August 3, 2013. The film received mixed reviews from critics and was a financial success, grossing over $269 million against a budget of $37 million. Roberts played the lead role in Gia Coppola's directorial debut, Palo Alto, based on James Franco's short story collection of the same name. The film was released on August 29, 2013. It received generally positive reviews, with particular praise for Roberts' performance. Tom Shone of The Guardian and Ian Freer of Empire both called her the "standout" of the film, with Freer praising her performance for being "heartbreaking as she suggests longings and anxieties without over-hyping it. Much like the film itself."Roberts next appeared in season three of the FX anthology horror series American Horror Story, called American Horror Story: Coven, in a main role from late 2013 through January 2014. Roberts portrayed a self-involved party girl named Madison Montgomery, who also happens to be a telekinetic witch. She then portrayed Maggie Esmerelda, a con artist posing as a fortune teller, in American Horror Story: Freak Show. In 2015, Roberts starred alongside Palo Alto co-star Nat Wolff in Ashby, portraying the supporting role of Eloise. The film had its world premiere at the Tribeca Film Festival on April 19, and was released on September 25, in a limited release and through video on demand. Roberts next appeared in the horror film The Blackcoat's Daughter (also known by its original title February) alongside Kiernan Shipka. Directed by Osgood Perkins, the film premiered at the 2015 Toronto International Film Festival. Roberts played the lead character Chanel Oberlin on Fox's comedy horror series Scream Queens, alongside Jamie Lee Curtis and Lea Michele. The series was created by American Horror Story producers Ryan Murphy and Brad Falchuk, with Glee producer Ian Brennan. The show was canceled after two seasons.
Roberts starred alongside Dave Franco in Lionsgate's adaptation of the young-adult novel Nerve. The film premiered at the SVA Theater on July 12, 2016, and grossed $85 million worldwide against its $19 million budget. In 2017, Roberts played Jess in the drama film Who We Are Now, released on September 9 at the 2017 Toronto International Film Festival. Later, Roberts returned to American Horror Story, guest starring as newscast reporter Serena Belinda, in its seventh season, Cult, in the episode "11/9". In March 2018, it was announced that Roberts was set to star in Anya's Ghost, an upcoming supernatural comedy film based on the award-winning graphic novel of the same name, written by Vera Brosgol and published in 2011. From April to August 2018, Roberts starred in three films: In a Relationship, Billionaire Boys Club, and Little Italy.
She next appeared in American Horror Story: Apocalypse, where she reprised her role of Madison Montgomery for the crossover season, returning to the main cast. On October 8, 2018, it was announced that Roberts had joined the cast of the animated musical comedy film UglyDolls, voicing the character Wedgehead. The film was released on May 3, 2019. In the same month, after reports about Roberts being cast as Kat Baker in the Netflix series Spinning Out, it was announced that she had exited the series due to scheduling conflicts. In 2019, Roberts starred in the fantasy drama film Paradise Hills, as Uma. The film had its world premiere at the Sundance Film Festival on January 26. From September through November 2019, Roberts starred in the ninth season of American Horror Story, subtitled 1984, portraying Brooke Thompson. The season has been described as being heavily influenced by classic horror slasher films such as Friday the 13th and Halloween.