Acting Burrows made her film debut in 1993 with a small role in
Jim Sheridan's
In the Name of the Father. Her first significant acting roles came in 1995, as an ambitious young Irishwoman in
Circle of Friends, and in
Ngozi Onwurah's
Welcome II The Terrordome. In 1996 she starred in the
BBC production of
Dennis Potter's
Karaoke and in
Hotel de Love; the next year she was seen in
Lovelife,
Nevada,
The Matchmaker and
Mike Figgis's
One Night Stand. In 1999 she appeared in Figgis's experimental film
The Loss of Sexual Innocence, in which she played twins – one raised in England, the other in Italy. In 1999, she appeared in the thriller
Deep Blue Sea, and had the title role in Figgis's film adaptation
Miss Julie, which premiered at the
Toronto International Film Festival. She starred for Figgis again alongside
Stellan Skarsgård in
Timecode (2000), a split-screen digital experimental film shot in a single take with no edits. She followed it with
Gangster No. 1, starring
Malcolm McDowell,
Paul Bettany and
David Thewlis. and starred in
Tempted, an improvised thriller set in New Orleans, with
Burt Reynolds and
Peter Facinelli. Figgis's ensemble feature
Hotel followed, reuniting Burrows with colleagues from
Timecode including
Salma Hayek and
Danny Huston on location in Venice, where she played the Duchess of Malfi. She had a cameo in
Frida, Hayek's 2002 biopic of artist
Frida Kahlo. Burrows performed in Spanish in
The Galindez File, a film written by Spanish novelist
Vazquez Montalban, about a woman seeking the truth about the disappearance of a critic of the
Dominican dictator Trujillo. In 2004, she played the role of
Andromache, the wife of Trojan Prince
Hector, played by
Eric Bana, in
Troy. Burrows dedicated herself to stage work in the early 2000s. She appeared at the
Royal National Theatre in
Jeanette Winterson's
The Powerbook, directed by
Deborah Warner; the play also went on tour, visiting the Theatre National Du Chaillot in Paris and the Teatro Argentina in Rome. In January 2005, she created the role of Janey Morris in the world premiere of
Earthly Paradise at the
Almeida Theatre. The play centered on the love triangle of Janey, her husband
William Morris (the writer and proponent of the
Arts and Crafts movement), and the
Pre-Raphaelite painter
Dante Gabriel Rossetti. London theatre critic Nicholas De Jongh said of her performance: "Burrows takes to the stage like a swan to water ... She deserves no end of watching." On 30 October 2005, she appeared on stage at the
Old Vic theatre in London in a rehearsed reading of the 24-hour play
Night Sky, alongside
Christopher Eccleston. Burrow has since participated in the "24 Hour Plays" in New York and Los Angeles. In 2006, Burrows was the female lead in the New Zealand thriller
Perfect Creature, appeared in
Hal Hartley's film
Fay Grim, and co-starred in
Klimt, Chilean director
Raoul Ruiz' cinematic portrait of
Gustav Klimt. Burrows played opposite
John Malkovich as the artist's lover, a woman of many personalities and nationalities. She then appeared in
Mike Binder's film
Reign Over Me with
Don Cheadle and
Adam Sandler. Burrows also had lead roles in the Indian thriller
Broken Thread and in director
Peter Howitt's drama
Dangerous Parking. She also had a starring role in Roger Donaldson's heist film
The Bank Job, and appeared opposite
Kevin Spacey in Jonas Pate's
Shrink. She contributed to an
Actors Come Clean for Congo video for the
Enough Project's campaign in support of
conflict mineral issues. In 2010, she starred as
Detective Serena Stevens on
Law & Order: Criminal Intent, departing at the end of the ninth season. In September 2010, she took part in the documentary feature
The People Speak, televised on the
History Channel. The film was directed and produced by
Colin Firth and Anthony Arnove. Burrows modelled for
Marks & Spencer's autumn 2010 campaign for their
Portfolio range. In 2012, she performed opposite
Rob Lowe in the political comedy
Knife Fight. She also starred in the
Amazon Video series
Mozart in the Jungle as Cynthia Taylor, a cellist with the New York Symphony. The series ran for four seasons from 2014 to 2018. In 2019, Burrows starred in the recurring role of
Dottie Quinn on the
second season of the
Netflix thriller
You. She reprised her role in the
third season, which was released in October 2021.
Writing Burrows has written diaries, book reviews and newspaper and magazine articles for
The Guardian,
The Independent, and
The Times and the
New Statesman. == Personal life ==