Theresa May's predecessor, David Cameron, says the outgoing PM should be "thanked for her tireless efforts on behalf of the country".

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"During the last three years of leading our nation through times of profound change and uncertainty, Theresa May has shown determination, resilience and a sense of public duty that has never wavered," says the Archbishop of Canterbury Justin Welby.

"That is a service to us all that deserves our admiration and gratitude.

"As Mrs May prepares to stand down from office over the coming months, this is a moment to pause and pray for her and her husband, Philip, whose support has been unwavering, and for all those around them working to ensure a smooth transition into new leadership."

The Conservative Party has set out the timeline of its next steps.

Mrs May will step down as Conservative Party leader on 7 June.

After that, nominations among MPs for the next leader will close in the week beginning 10 June, the party says.

Rounds of voting will take place until the candidates are narrowed down to a final two.

"We expect that process to be concluded by the end of June, allowing for a series of hustings around the UK for members to meet and question the candidates, then cast their votes in time for the result to be announced before Parliament rises for the summer," the party statement added.

The BBC's Europe editor says European Commission President Jean-Claude Juncker described Mrs May as a woman "of great courage".

The first edition of today's Evening Standard newspaper focuses, unsurprisingly, on the PM's resignation.

The front page features a tearful Mrs May alongside the headline: "I've done all I can."

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When Theresa May became prime minister in July 2016 she identified seven "burning injustices".

Almost three years on, the Reality Check team looks at whether she achieved her policy goals.

BBC News Channel

Tory Brexiter Mark Francois, a big critic of Theresa May, says he felt sympathy for her but he would admit he "never thought she was a great prime minister".

He adds that entering cross-party Brexit talks with Jeremy Corbyn was the "final straw" for many Conservative MPs.

"Unfortunately, the Dancing Queen has met her Waterloo", he says.

He adds that the next Tory leader will "almost certainly" be a Brexiteer, and he is "quite tempted" to vote for fellow Leave-voting MP Steve Baker.

Former Danish PM speaks to BBC Radio 4 about her tips for life after being prime minister.

"I started by getting my bike fixed... and then I watched a lot of Game of Thrones."

European Commission President Jean-Claude Juncker "followed prime minister May's announcement this morning without personal joy", a spokeswoman has said.

She added: "The president very much liked and appreciated working with prime minister May, and has said before Theresa May is a woman of courage for whom he has great respect.

"He will equally respect and establish working relations with any new prime minister, whomever they may be, without stopping his conversations with prime minister May.

"Our position on the withdrawal agreement has been set out by my colleague yesterday. There is no change to that.

"We have set out our position on the withdrawal agreement and on the political declaration.

"The European Commission and the Article 50 format has set out its position and we remain available for anyone who will be the new prime minister."

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The Evening Standard - edited by former Chancellor George Osborne - says Theresa May leaves Downing Street as "one of the shortest serving and least successful prime ministers in Britain’s history".

The editorial says, external Mrs May was "a divider, when she should have been a unifier" and criticises the PM for using "harsh language about 'traitors' and 'saboteurs'".

It describes her red lines over negotiating Brexit as "foolish" and says she "never levelled with the British people about the the trade-offs that Brexit entailed until it was far too late".

Candidates must be nominated by two Tory MPs.

If only one candidate comes forward, they become leader automatically - but in this case it looks like there will be many hats thrown into the ring.

The list of candidates is whittled down to a shortlist of two in a series of votes by Conservative MPs.

The final pair then go to a postal ballot of all party members before the winner is crowned.

The winning politician will become Conservative Party leader and, by default, prime minister.

In a statement, Mayor of London Sadiq Khan said he does not agree with Mrs May on much "but I have some sympathy with her today".

He added: "Her extremely difficult job was made impossible by the Brexit extremists in the Conservative Party.

"It is totally unacceptable for Britain's future to be decided by these same people."

The Labour mayor wants Article 50 to be revoked - meaning Brexit would be cancelled.

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Theresa May will step down as leader of the Conservative Party on 7 June.

That will formally start a race to replace her. But while that race for a successor is ongoing, Mrs May will remain as prime minister. For how long, we don't know.

How long could the leadership contest take?

The timetable is the responsibility of Sir Graham Brady, the chairman of the 1922 Committee of Tory backbenchers.

It is expected to last around 12 weeks - but could be shortened due to the need to crack on with Brexit.

But a new leader is likely to be in place by the Conservative Party conference, which this year begins on 29 September.

When David Cameron quit as leader in 2016 following the EU referendum result, the contest was originally planned to end in early September that year. But it took far less time, since Mrs May was the last candidate standing and became PM on 13 July.

Because the Brexit extension is set to last until 31 October, the party could decide to have a short race to give the leader time.

Allen Cook
BBC News

Conservative MPs in the West Midlands have praised Theresa May after she said she would quit as Conservative leader on 7 June.

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The move paves the way for a contest to decide a new prime minister although she will continue in the role while the Tories decide who that is.

One of the potential contenders in that leadership contest, Home Secretary and Bromsgrove MP Sajid Javid, tweeted , externalthat "nobody could have worked harder" as PM.

Rachel Maclean, MP for Redditch, said that while she was sad to see Mrs May go, she saw it as a "good opportunity" to deliver Brexit. , external

North Shropshire MP Owen Paterson's reaction to the resignation was: "Good, we can now get on with choosing a new leader.”

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Silvia Dall’Angelo, senior economist at Hermes Investment Management, believes an early general election is possible.

"The risk is that under the next leader - most likely coming from the intransigent Eurosceptic wing of the Tory party - the institutional tensions between the executive and Parliament will intensify, potentially generating an even more fragmented and dysfunctional political landscape.

"The next stage will probably result in early general elections, but other outcomes are possible, including a second referendum and a no-deal Brexit (the latter being the default scenario under current Brexit legislation).

"At any rate, the Brexit situation is unlikely to be resolved any time soon, and uncertainty will persist, which will continue to weigh on the country’s economic prospects and financial assets," she says.