The race for Number 10 is heating up as several prominent Tories have thrown their hats in the ring for the top job.
Here are the main runners and riders, where they stand on Brexit and what they have had to say about their bid to take on the mantle of Conservative leader.
– Boris Johnson
The former foreign secretary and London mayor is considered by most as the favourite to win the leadership race (Ladbrokes 11/10).
Easily recognisable, the 54-year-old nearly beat Theresa May to the top job in 2016, until Michael Gove decided to scupper his chances.
Since then, Mr Johnson has burnished his Leave credentials by walking out of Cabinet alongside David Davis in July last year, and has also cleared the decks on a notoriously complicated personal life.
In a speech in Switzerland on Friday, he vowed to take Britain out of the EU on October 31, "deal or no deal", if he is made PM.
Backers include Johnny Mercer, Karl McCartney, and Nadine Dorries.
– Dominic Raab
The former Brexit secretary formally entered the Tory leadership race over the weekend with a call for a "new direction" (Coral 5/1).
The 44-year-old told the Mail on Sunday he would prefer to leave the EU with a deal, but said the UK must "calmly demonstrate unflinching resolve to leave in October – at the latest".
The MP for Esher and Walton added: "The country now feels stuck in the mud, humiliated by Brussels and incapable of finding a way forward.
"The Prime Minister has announced her resignation. It's time for a new direction."
Mr Raab was a prominent Brexiteer in the referendum campaign and Mrs May appointed him as her second Brexit secretary in July, but he quit the role in November, saying he could not support her eventual deal.
Helen Grant has announced her support.
– Jeremy Hunt
The Foreign Secretary campaigned for Remain in the 2016 referendum and would be a moderate candidate on Brexit in the leadership election (Ladbrokes 12/1).
The 52-year-old battled with doctors as health secretary before being appointed Foreign Secretary in July last year, when Mr Johnson quit.
Mr Hunt claimed his business background would help resolve Brexit, telling the Sunday Times: "If I was prime minister, I'd be the first prime minister in living memory who has been an entrepreneur by background.
"Doing deals is my bread and butter as someone who has set up their own business."
David Morris has said he is supporting Mr Hunt.
– Rory Stewart
The new International Development Secretary launched his leadership bid in an interview with The Spectator last month (Coral 12/1).
Mr Stewart, a former environment minister and prisons minister, has been scathing of Mr Johnson's stance on Brexit, saying a no-deal Brexit would be "a huge mistake, damaging, unnecessary, and I think also dishonest".
In what is likely to be seen by many as a dig at Mr Johnson, the 46-year-old MP for Penrith and The Border tweeted: "The star name will not always be the best choice. There may be times when Jiminy Cricket would make a better leader than Pinocchio."
Mr Stewart's campaign was endorsed by Sir Nicholas Soames, grandson of former Prime Minister Sir Winston Churchill.
– Esther McVey
Former work and pensions secretary Ester McVey announced her leadership bid as she hosted an LBC call-in on Friday (Ladbrokes 66/1).
The former television presenter-turned MP for Tatton, who quit Mrs May's Cabinet in November in protest over her Brexit plan, told listeners that the UK should be prepared to leave the EU without a deal.
Writing in the Sunday Telegraph, the 51-year-old said: "This country needs a genuinely bold, new approach. So we must now leave the EU on October 31 with a clean break.
"It's time to recapture that optimism which brought about the referendum result, provide the country with a clear direction and deliver the clean Brexit people voted for," she added.
Backers include Pauline Latham and Ben Bradley.
– Matt Hancock
Health Secretary Matt Hancock waited until Saturday morning to announce that he was in the running (Betfred 25/1).
The 40-year-old said he was throwing his hat in the ring because the party needed to look to the future and attract younger voters.
He said he would take a different approach to the one Theresa May used in order to get Commons support for a Brexit deal.
He said: "She didn't start by levelling with people about the trade-offs.
"I think it is much, much easier to bring people together behind a proposal if you are straightforward in advance."
He told the BBC that a no-deal Brexit "simply won't be allowed by Parliament".
Backers include Maggie Throup and Bim Afolami.
– Andrea Leadsom
Former leader of the House of Commons, Andrea Leadsom, formally entered the race over the weekend, telling the Sunday Times that, if she is elected PM, the UK would quit the EU in October with or without a deal (Betfred 20/1).
The MP for South Northamptonshire said: "To succeed in a negotiation you have to be prepared to walk away."
The 56-year-old added that she would introduce a citizens' rights Bill to resolve uncertainty facing EU nationals, then seek agreement in other areas where consensus already exists, such as on reciprocal healthcare and Gibraltar.
She has previously described the UK's continued membership of the EU as "disgusting" and claimed that a Eurosceptic prime minister would have delivered Brexit already.
– Michael Gove
The Environment Secretary announced on Sunday that he is running to be next prime minister (Ladbrokes 8/1).
Mr Gove is posing as a self-styled "unity candidate".
"I believe that I'm ready to unite the Conservative and Unionist Party, ready to deliver Brexit, and ready to lead this great country," he said.
His intervention is likely to cause concern to current front-runner Boris Johnson, after a spectacular falling-out between the two former allies in the 2016 leadership contest helped destroy both men's chances of the top job.
Mr Gove has made some memorable Commons appearances, notably in defence of Mrs May's deal, and has a reputation for mastering complicated briefs.
Backers include Nick Gibb, Kevin Hollinrake, John Stevenson, Sir Edward Leigh, Bob Seely.
– Sajid Javid
Home Secretary Sajid Javid announced his leadership bid in a video he tweeted on Monday (Ladbrokes 25/1).
Highlighting the Tories' poor performance in the European elections, Mr Javid said his party "must get on and deliver Brexit".
"It's time to rebuild trust, find unity and create new opportunities across the UK," he said.
Mr Javid had previously signalled his leadership ambitions by arguing that he wanted the Tories to be the party of social mobility, in an interview with The Spectator.
The 49-year-old, who backed Remain in the referendum but has since positioned himself as a firm Leaver, became the first home secretary from an ethnic minority background when he was appointed in April 2018.
The son of a Pakistani bus driver from Rochdale, he was a managing director at Deutsche Bank before becoming an MP in 2010.
Robert Halfon and John Glen have announced their support.
We need a Leader who is electable, can unify the country, and who embodies the Conservative spirit of the ladder of opportunity. That's why I'm backing @sajidjavid for the job. pic.twitter.com/dOT2t7TvQ7
— Robert Halfon MP #WorkingHard4Harlow (@halfon4harlowMP) May 24, 2019
– Kit Malthouse
Housing Minister Kit Malthouse outlined why he believes he is the best candidate for the job in an article in The Sun newspaper (William Hill 66/1).
Mr Malthouse, widely credited as the convener of both Conservative Leavers and Remainers to develop a compromise on Mrs May's withdrawal agreement, said there was a "yearning for change".
The 52-year-old MP for North West Hampshire is a former deputy mayor of London and entered the Commons in 2015 as David Cameron's Conservatives won a majority.
His name was given to the so-called Malthouse Compromise – a proposal drawn up by backbenchers from Leave and Remain wings of the Tory Party, which would have implemented Mrs May's Brexit deal with the backstop replaced by alternative arrangements.
Writing in The Sun, he said: "We need to end the Brexit paralysis, and while I voted to leave the EU, I know that without unity across the UK, we cannot get a deal over the line."
– Sir Graham Brady
Sir Graham Brady quit as the leader of the 1922 Committee – a position which gave him a significant role in the Prime Minister's departure – on Friday in order to consider a leadership bid (Ladbrokes 33/1).
The MP for Altrincham and Sale West had chaired the Tory backbench committee for nearly 10 years, having held shadow cabinet positions under David Cameron while in opposition.
The 52-year-old told the Sunday Times the only way to regain people's trust is by leaving the EU by October 31.
– Penny Mordaunt
Penny Mordaunt became the UK's first female Defence Secretary at the start of the month, following the sacking of Gavin Williamson (Bet365 22/1).
The 45-year-old Royal Navy reservist has been named by Jacob Rees-Mogg as one of his favoured candidates and has a higher public profile than most due to her 2014 appearance on reality TV show Splash!
MP for Portsmouth North since 2010, she supported Mrs Leadsom in the 2016 Conservative leadership contest.