Labour Leader Jeremy Corbyn has said he understood the "stress" Theresa May was under, but did not recognise her “description of the country” in her statement.

In a clip for broadcasters, he says her decision to step down was the right one, adding that she "clearly cannot command a majority in Parliament".

He adds that Theresa May “wasn’t really offering concessions” during the cross-party talks with Labour that broke down last week.

He says a new Tory leader "isn't going to solve the problem", and that the first thing the new PM should do is call an election, adding that a Conservative government was “untenable”.

Asked whether the case for another Brexit referendum has grown due to her departure, he was non-committal.

"I think the time to discuss that is when we can see the direction in which the offers are going to be put one way or the other."

The Austrian chancellor has also reacted to Mrs May's announcement, calling for an "orderly" Brexit, in a nod to Conservatives pushing for a no deal departure from the EU.

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Irish Prime Minister Leo Varadkar has paid tribute to Mrs May, saying he will miss her and her team.

Speaking after voting in the European elections in his local polling station in Dublin, Mr Varadkar said: "I am very sorry to hear of the resignation of prime minister May today.

"We will certainly miss her and miss her team. We worked very closely on issues over the past one-and-a-half years on Brexit and the north [of Ireland].

"I particularly want to pay tribute to her to agreeing to retain and strengthen the common travel area.

"As a result of the agreement we made, British and Irish citizens are able to live, work, study, travel and access health care, housing, education and welfare and pensions in each other's countries as though we are citizens of both."

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Pro-EU Conservative MP Ken Clarke has stood for the leadership of the Conservative Party three times before.

When asked if he is tempted to add his name to an already crowded list to succeed Mrs May, he replies: "I think I’ll give it a miss."

"There has to be at least one Tory MP who doesn’t run," he jokes.

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Britain's second female prime minister, like the first, has ultimately been brought down by Conservative in-fighting over Europe.

But Theresa May is unlikely to join Margaret Thatcher in the annals of leaders who left an indelible mark on their country - at least not in the way she might have hoped when entering Downing Street in 2016.

Whatever ambitions she had - to reach out to the forgotten parts of the nation, or correct the "burning injustices" in British society - were overshadowed by a single word: Brexit.

Read more here.

Nick Boles - who resigned from the Conservative Party in April - says a new leader will not be enough to move the UK forward.

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Discussing the future leader of the Conservative Party, Tory MP Nicky Morgan, a former education secretary who voted Remain, says that "someone who actively wants no-deal Brexit would struggle to get support from a lot of people in the party".

"There will be someone to find a way through," she adds.

Mrs May has developed a reputation for surviving in almost impossible circumstances, but she is still among the UK prime ministers with the shortest time in office.

Here are five other charts on Mrs May's time in office.

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Conservative MP Brexiteer Mark Francois is asked about making apparent throat slitting gestures during Prime Minister's Questions on Wednesday - a move that attracted criticism.

"What I meant was - it is all over," he says.

"You could sense her authority draining away."

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Conservative grandee Ken Clarke, a former chancellor, has his say on the Tory party's treatment of their PM.

The reaction to Theresa May's resignation announcement continues to pour in.

This time it's the turn of senior German MEP Manfred Weber, calling for the UK to take a "constructive approach" to the unresolved issue of Brexit.

Labour leader Jeremy Corbyn says that, whoever becomes the new Tory leader, a general election must now be called.

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When asked if he feels sympathy towards the prime minister, Guardian columnist Owen Jones replies: "I think of the people she has cruelly treated."

"If any sympathy is to be extended, it should be to the Windrush Britons who because of her were kicked out of their homes, to the children driven into poverty at the fastest rate since 1998, to the disabled having their benefits stripped away, to the victims of universal credit whose lives have been destroyed," he says.

"I wish we extended sympathy to them rather than the powerful."

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Conservative MP Robert Halfon, who served as a minister under Mrs May, says the prime minister "did a lot of good things for our country".

The result of the 2017 general election, he says, put her in a "difficult situation", whilst Brexit "has been impossible to deliver".

She was nevertheless "devoted to public service", he adds.

Chris Morris
BBC Reality Check

One of the themes of Theresa May’s resignation speech was the need to find a compromise on Brexit.

But her own record as prime minister suggests that she only took this message on board when it was too late.

In her first party conference speech in October 2016, she promised to end the free movement of people from the EU, end the role of the European Court of Justice in the UK, and take the country out of the single market and the customs union; all while maintaining frictionless trade with the EU.

She also triggered Article 50 negotiations on Brexit, under pressure from her own party, before any consensus had been found on what the UK really wanted. “No deal is better than a bad deal” became her mantra.

Only after more than a year of difficult negotiations did the idea of compromise come to the fore. But by then the political divisions surrounding Brexit had become entrenched, partly as a result of the prime minister’s own policy choices.

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As Theresa May announces her departure, where did things go wrong for her?

Andrea Leadsom, who resigned from government on Wednesday evening, has her say on Mrs May's announcement.