Eve was born in London, England, the daughter of actors Trevor Eve and Sharon Maughan. She has two younger brothers, Jack and George. Eve is of English, Welsh, and Irish descent.

She attended Bedales School and then took her A-Levels at Westminster School in London. During her gap year, she studied at the Beverly Hills Playhouse and then read English at St Catherine's College, Oxford. While at Oxford, she appeared in student productions of The Importance of Being Earnest, Animal Crackers (which toured to the Edinburgh Fringe Festival), Scenes from an Execution and The Colour of Justice.

Eve has appeared in television dramas such as the BBC's The Rotters' Club, Agatha Christie's Poirot and Hawking[5] and starred in the film Stage Beauty (2004).

In 2006, she starred in two comedic films: Starter for 10 and Big Nothing (in which she and co-star Simon Pegg put on American accents). She spent the early part of 2006 in India working on a drama mini-series Losing Gemma about backpackers.

On the stage, Eve has appeared in two plays directed by Trevor Nunn. In 2006, she played the young Esme in the new Tom Stoppard play Rock 'n' Roll, at the Royal Court Theatre, later reprising her role for the 2007 Broadway transfer. For this performance, she was nominated for the best supporting actress award at the Whatsonstage.com Theatregoers' Choice Awards. In 2009, she played Roxane in a production of Cyrano de Bergerac at the Chichester Festival Theatre.

In 2010, Eve played the female lead in the American romantic comedy She's Out of My League, in which her parents play the roles of her character's parents. She also played the role of Erin, Charlotte's Irish nanny, in Sex and the City 2.

During 2011, Eve had a recurring guest role in season 8 of the HBO series Entourage, as Sophia, a journalist and love interest to Vincent Chase. She played the role of Dr. Carol Marcus in Star Trek Into Darkness, released 17 May 2013.

Eve took part in the opening session of the 2013 Consumer Electronics Show.

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