Rigg was born in Doncaster, which was then in the West Riding of Yorkshire, now in South Yorkshire to Louis Rigg (1903–1968) and Beryl Hilda (née Helliwell; 1908–1981); her father was a railway engineer who had been born in Yorkshire. Between the ages of two months and eight years Rigg lived in Bikaner, India, where her father was employed as a railway executive.
Hindi was her second language in those young years (and she used to enjoy using a smattering of words and phrases when ordering Indian food). She was then sent to a boarding school, the Moravian School in Fulneck, near Pudsey. She disliked her boarding school, where she felt like a fish out of water, but she believed that Yorkshire played a greater part in shaping her character than India did. She trained as an actress at the Royal Academy of Dramatic Art from 1955–57, where her classmates included Glenda Jackson and Siân Phillips.
Rigg's career in film, television and the theatre has been wide-ranging, including roles in the Royal Shakespeare Company between 1959 and 1964. Her professional debut was in the RADA production of The Caucasian Chalk Circle at the York Festival in 1957. Her role was Natasha Abashwilli.
She returned to the stage in the Ronald Millar play Abelard and Heloïse in London in 1970, and made her Broadway debut with the play in 1971, earning the first of three Tony Award nominations for Best Actress in a Play. She received her second nomination in 1975, for The Misanthrope. A member of the National Theatre Company at the Old Vic from 1972 to 1975, Rigg took leading roles in premiere productions of two Tom Stoppard plays, Dorothy Moore in Jumpers (National Theatre, 1972) and Ruth Carson in Night and Day (Phoenix Theatre, 1978).
In 1982, she appeared in a musical called Colette, based on the life of the French writer and created by Tom Jones and Harvey Schmidt, but it closed during an American tour en route to Broadway. In 1987 she took a leading role in the West End production of Stephen Sondheim's musical Follies. In the 1990s, she had triumphs with roles at the Almeida Theatre in Islington, including Medea in 1992 (which transferred to the Wyndham's Theatre in 1993 and then Broadway in 1994, for which she received the Tony Award for Best Actress), Mother Courage at the National Theatre in 1995 and Who's Afraid of Virginia Woolf? at the Almeida Theatre in 1996 (which transferred to the Aldwych Theatre in 1997).
In 2004, she appeared as Violet Venable in Sheffield Theatres' production of Tennessee Williams's play Suddenly Last Summer, which transferred to the Albery Theatre. In 2006, she appeared at the Wyndham's Theatre in London's West End in a drama entitled Honour which had a limited but successful run. In 2007, she appeared as Huma Rojo in the Old Vic's production of All About My Mother, adapted by Samuel Adamson and based on the film of the same title directed by Pedro Almodóvar.
She appeared in 2008 in The Cherry Orchard at the Chichester Festival Theatre, returning there in 2009 to star in Noël Coward's Hay Fever. In 2011 she played Mrs Higgins in Pygmalion at the Garrick Theatre, opposite Rupert Everett and Kara Tointon, having played Eliza Doolittle 37 years earlier at the Albery Theatre.
Rigg appeared in the British 1960s television series The Avengers (1965–68) playing the secret agent Mrs Emma Peel in 51 episodes, replacing Elizabeth Shepherd at very short notice when Shepherd was dropped from the role after filming two episodes. Rigg auditioned for the role of Emma Peel on a whim, without ever having seen the programme. Although she was hugely successful in the series, she disliked the lack of privacy that it brought. She also did not like the way that she was treated by the Associated British Corporation (ABC). After a dozen episodes she discovered that she was being paid less than a cameraman. For her second season she held out for a pay rise from £150 a week to £450, but there was still no question of her staying for a third year. Patrick Macnee, her co-star in the series, noted that Rigg had later told him that she considered Macnee and her driver to be her only friends on the set.
On the big screen she became a Bond girl in On Her Majesty's Secret Service (1969), playing Tracy Bond, James Bond's only wife, opposite George Lazenby. She said she took the role with the hope that she would become better known in the United States.
Her other films from this period include The Assassination Bureau (1969), Julius Caesar (1970), The Hospital (1971), Theatre of Blood (1973), In This House of Brede (1975), based on the book by Rumer Godden, and A Little Night Music (1977). She appeared as the title character in The Marquise (1980), a television adaptation of play by Noël Coward. She appeared in the Yorkshire Television production of Ibsen's Hedda Gabler (1981) in the title role, and as Lady Holiday in the film The Great Muppet Caper (also 1981). The following year she received acclaim for her performance as Arlena Marshall in the film adaptation of Agatha Christie's Evil Under the Sun, sharing barbs with her character's old rival, played by Maggie Smith.
She appeared as Regan, the king's treacherous second daughter, in a Granada Television production of King Lear (1983), which stars Laurence Olivier in the title role. As Lady Dedlock she costarred with Denholm Elliot in a television version of Dickens' Bleak House (BBC, 1985), and played the Evil Queen, Snow White's evil stepmother, in the Cannon Movie Tales's film adaptation of Snow White (1987). In 1989 she played Helena Vesey in Mother Love for the BBC; her portrayal of an obsessive mother who was prepared to do anything, even murder, to keep control of her son won Rigg the 1989 BAFTA for Best Television Actress.
In the 1990s, she appeared on television as Mrs. Danvers in Rebecca (1997), winning an Emmy, as well as the PBS production Moll Flanders, and as the amateur detective Mrs. Bradley in The Mrs Bradley Mysteries. In this BBC series, first aired in 2000, she played Gladys Mitchell's detective, Dame Beatrice Adela Le Strange Bradley, an eccentric old woman who worked for Scotland Yard as a pathologist. The series was not a critical success and did not return for a second season.
From 1989 until 2003, she hosted the PBS television series Mystery!, shown in the United States by PBS broadcaster WGBH, taking over from Vincent Price, her co-star in Theatre of Blood. Her TV career in America has been varied. She starred in her own sitcom Diana (1973), but it was not successful.
She also appeared in the second series of Ricky Gervais's comedy Extras, alongside Harry Potter star Daniel Radcliffe, and in the 2006 film The Painted Veil.
In 2013 she appeared in an episode of Doctor Who in a Victorian-era based story called "The Crimson Horror" alongside her daughter Rachael Stirling, Matt Smith and Jenna-Louise Coleman. The episode had been specially written for her and her daughter by Mark Gatiss and aired as part of series 7. It was not the first time mother and daughter had appeared in the same production – that was in the 2000 NBC film In the Beginning – but the first time she had worked with her daughter and also the first time in her career her roots were accessed to find a Doncaster, Yorkshire, accent.
The same year, Rigg secured a recurring role in the third season of the HBO series Game of Thrones, portraying Lady Olenna Tyrell, a witty and sarcastic political mastermind popularly known as the Queen of Thorns, the grandmother of regular character Margaery Tyrell.
Her performance was well received by critics and audiences alike, and earned her an Emmy nomination for Outstanding Guest Actress in a Drama Series for the 65th Primetime Emmy Awards in 2013.
She reprised her role in season four of Game of Thrones, and in July 2014 received another Guest Actress Emmy nomination. In 2015 and 2016, she again reprised the role in seasons five and six in an expanded role from the books. The character was finally killed off in the seventh season, with Rigg's final performance receiving critical acclaim.
In the 1960s, Rigg lived for eight years with director Philip Saville, gaining attention in the tabloids when she disclaimed interest in marrying the older, already-married Saville, saying she had no desire "to be respectable". She was married to Menachem Gueffen, an Israeli painter, from 1973 until their divorce in 1976, and to Archibald Stirling, a theatrical producer and former officer in the Scots Guards, from 25 March 1982, until their divorce in 1990. With Stirling, Rigg has a daughter, actress Rachael Stirling, who was born in 1977.
Rigg has long been an outspoken critic of feminism, saying in 1969, "Women are in a much stronger position than men."
Rigg is a Patron of International Care & Relief and was for many years the public face of the charity's child sponsorship scheme. She was also chancellor of the University of Stirling, being succeeded by James Naughtie when her ten-year term of office ended on 31 July 2008.
Michael Parkinson, who first interviewed Rigg in 1972, described her as the most desirable woman he ever met, who "radiated a lustrous beauty". A smoker from the age of 18, Rigg was still smoking 20 cigarettes a day in 2009. In 2011, she said she had given up smoking because she "had to".
Rigg received honorary degrees from the University of Stirling in 1988 and the University of Leeds in 1992.
Rigg was made a Commander of the Order of the British Empire (CBE) in the 1988 New Year Honours and a Dame Commander of the Order of the British Empire (DBE) in the 1994 Birthday Honours.
In 2014, Rigg received the Will Award, presented by the Shakespeare Theatre Company, along with Stacey Keach and John Hurt.
On 25 October 2015, to mark 50 years of Emma Peel, the BFI (British Film Institute) screened an episode of The Avengers followed by an onstage interview with Rigg about her time in the television series.