After winning the confidence vote from her party this week, Theresa May says she won't stay on to lead the Tories into the next general election.

Mrs May's pledge may have helped secure her immediate future - she can't be challenged in the same way by MPs for a year - but the long term is far from certain.

Does her concession strengthen her hand for the difficult months ahead or is a swift departure now inevitable?

And how did other prime ministers in similar situations fare? Read more here.

Here are key excerpts from Theresa May's statement on Brexit, which she read out at her Brussels press conference:

• "I was crystal clear about the assurances which are needed on the backstop, having heard the views of MPs in the House of Commons"
• "I reiterated that it is in the interests of the EU as well as the UK to get this over the line. A disorderly Brexit would be good for no-one..."
• "As formal conclusions, these [EU] commitments have legal status and therefore should be welcomed."
• "As I have always said, the guaranteed way of avoiding the backstop is to have the future partnership in place by the time the implementation period is over. The EU is very firmly committed to this course."
• "But MPs will require further assurances, and I have discussed that this morning with my EU partners, including Presidents Tusk, Juncker and others."
• "I note there has been reporting that the EU is not willing to consider any further clarification. The EU is clear – as I am – that if we are going to leave with a deal this is it."
• "But my discussions with colleagues today have shown that further clarification and discussion following the Council’s conclusions is in fact possible."
• "There is work still to do and we will be holding talks in coming days about how to obtain the further assurances that the UK Parliament needs in order to be able to approve the deal."
• "I say again. It is in the overwhelming interest of all our people – in the EU and the UK – to get this done, and as quickly as possible."

The Brussels political think-tank Bruegel argues that a second Brexit referendum, external would clarify things and break the parliamentary deadlock.

Theresa May has however ruled out holding a second referendum.

Theresa May was asked by one reporter at her Brussels press conference if she'd had a "trying week" - raising a smile and a reply from the PM of: "Has something happened this week?", to laughter from the room.

When he replied he'd "read reports", she said "ah - you shouldn't believe everything you read in the newspapers".

Saying it was a "trying week" was an understatement to say the least, what with the vote of confidence followed by this Brussels summit.

Mrs May was asked if her party problems at home, and the wranglings with the EU, had made her want to pack the whole thing in, throw away her phone and move to a remote island.

But she replied there was a "job to be done" and that it was "our duty as a government and as a Parliament" to see Brexit through and "build a brighter future for Britain".

As we wait for the further press conferences this afternoon, it might be time to catch up on what is happening with Brexit.

And for that matter, what it actually is.

We've got a simple guide here.

Here's the moment Theresa May was asked about the conversation she had Jean-Claude Juncker earlier that was captured on cameras.

We're expecting further press conferences on Friday afternoon by:

European Council President Donald Tusk and EU Commission President Jean-Claude Juncker (jointly); French President Emmanuel Macron and German Chancellor Angela Merkel.

Image source, Reuters

Theresa May has said it is still possible to get the assurances MPs need to back her Brexit deal despite EU leaders ruling out any renegotiation.

Speaking at a summit in Brussels, she said there was still "work to do" but there had been progress and talks over "further clarification" would continue.

The UK PM admitted having a "robust" discussion with European Commission President Jean-Claude Juncker.

He urged more clarity from the UK after "nebulous and imprecise" debate.

Read our full story here.

Here are a few more lines from that press conference in Brussels, which has just finished.

Mrs May says that it's in the interests of the EU as well as the UK to get this over the line, saying a "disorderly Brexit" is good for no one.

She believes that further clarification is, in fact, possible.

And she says if the backstop is triggered, it would only be a temporary move.

But it's clear there is "work still to do" with more talks to find the assurances that the UK Parliament needs.

ITV's political editor Robert Peston has given his thoughts on what went wrong for Theresa May - and how it went wrong.

In a Facebook post, external, he wrote: "Here is the measure of Theresa May’s failure last night - according to an observer of her request to EU leaders for 'assurances' that UK membership of the EU backstop would be finite and of short duration.

"They were ready to help. They assumed a process of officials agreeing a text over coming week would start today, to give her the necessary words that would persuade Tory and DUP critics of her deal to ultimately support it.

"But it was during the course of questioning her that they concluded such a process - such an extension of talks - would be a total waste of time. Why?

"Well according to one observer of the conversation between May and the EU27 leaders, 'she could not say what would actually deliver a majority in parliament for her'.

"Why on earth could and should they start talks in the absence of knowing what May actually wants?"

The PM said she welcomed commitments by the EU27 to get a new trade deal completed quickly so that the backstop would be needed.

As formal conclusions that have "legal status", she added.

But Mrs May said it's clear "further clarification and discussion is possible".