1. Eve was born in London, the daughter of actors Trevor Eve and Sharon Maughan. and More House School, and then took her A-levels at Westminster School in London.
2. While at Oxford, she appeared in student productions of The Importance of Being Earnest, Animal Crackers , Scenes from an Execution and The Colour of Justice.
3. On the stage, Eve has appeared in two plays directed by Trevor Nunn.
4. In 2009, she played Roxane in a production of Cyrano de Bergerac at the Chichester Festival Theatre.
5. 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. 2011 Eve also portrayed Hollywood actress Lara Tyler in the romantic comedy The Decoy Bride.
6. Eve is also known for her role of Dr. Carol Marcus in Star Trek Into Darkness.
7. In 2012, she played the younger 1969 version of Agent O in Men In Black 3, the older version being played by Emma Thompson.
8. In 2013, she co-starred in Before We Go with Chris Evans, who also directed the film. She played herself in the Hollywood film Night at the Museum: Secret of the Tomb in 2014 and has since starred in several productions, including Criminal in 2016.
9. In 2016, ela apareceu em “Nosedive”, an episode of the anthology series Black Mirror.
10. On 14 August 2014, Eve announced her engagement to her “high school sweetheart”, financier Alex Cowper-Smith. They separated in April, 2017.
11. She has heterochromia, a condition that causes the irises of both eyes to be different colors.