A guide to how the UK will leave the European Union following the 23 June referendum vote.Read more
It's been the first day of negotiations between the UK and the EU over Brexit.
Brexit Secretary David Davis said talks got off to a "promising start".
The EU's chief negotiator Michel Barnier said there would be "substantial" consequences from Brexit, but that he was not looking to punish the UK.
The initial focus will be on expat rights, a financial settlement and "other separation issues".
In other news, Theresa May chaired a meeting of the Cobra security committee after the terror attack close to the Finsbury Park Mosque in north London.
She also welcomed the new Irish Prime Minister Leo Varadkar to Downing Street. He said he had been "reassured" about the potential deal between the Conservatives and the DUP.
Four separate government ministers were warned that fire regulations were not keeping people safe, in letters that have subsequently been seen by the BBC.
In the leaked letters, experts warn that those living in tower blocks like Grenfell Tower were "at risk",the BBC's Panorama programme says.
At least 79 people are dead or missing presumed dead after the fire at the London high-rise last week.
The department that received the letters said work to improve regulation and safety had already been under way.
"Theresa May will cling on, but the election result changes everything. Brexit and the future of both great parties hang in the balance," writes Andrew Marr in The New Statesman.
The BBC presenter predicts that the Conservatives will not want to risk going through another election against Jeremy Corbyn so will not mount a challenge to Theresa May's leadership.
As for Labour, he says the party might get many of the things it wanted, despite not winning the election and that "one way or another, the grumpy rebel talent that turned its back on Jeremy Corbyn must be allowed to shuffle back".
BBC News Channel
There has been much talk of the friendly tone between the Brexit Secretary David Davis and the chief EU negotiator Michel Barnier at the news conference earlier.
BBC correspondent in Brussels Christian Fraser says the personal relationship will count for a great deal because the men are driving the process, but says they are facing "seemingly insurmountable issues to deal with in two years".
He says the "pace is picking up but there is an awful lot to do in a short period of time" - 500 days - and that while the two men will meet for a week every month, technical teams will be doing the preparatory work.
The Lib Dem leader Tim Farron has accused the Brexit Secretary David Davis of caving in on day one of the talks about Britain leaving the EU.
David Davis said the row of the summer would be over the sequencing of Brexit talks, and one day in he has capitulated. The man is a joker. Despite the Government's posturing, the EU was clear today it has not made a single concession to David Davis. He has been utterly humiliated."
Brexit negotiations between the UK and the EU have officially begun - and so has BBC Radio 5 Live's new podcast. We’ll be following the twists and turns of the talks and bringing you all the behind-the-scenes developments from Westminster and Brussels.
You can find the podcast here.
Earlier, Theresa May welcomed the new Irish Prime Minister for talks in Downing Street.
Afterwards, Leo Varadkar said he felt reassured by what he had heard from Mrs May about a potential deal between the Democratic Unionist Party and the Conservatives.
On Brexit, he said he hoped that any border between the two countries would be "invisible" and that citizens' rights would remain the same.
But what do we know about the new Taoiseach - the youngest person ever to hold the post?
Find out here.
A quick re-cap of the news conference from Brussels, after the first day of formal talks on Brexit.
Negotiations between the UK and the EU have got off to a "promising start", Brexit Secretary David Davis says.
The initial focus will be on citizens' rights, a financial settlement and "other separation issues".
Discussions aimed at preserving the Good Friday Agreement and common travel area in Ireland will also begin.
Michel Barnier says it is not a matter of the EU making concessions or looking to punish the UK for its decision to leave the EU. This fits in with the general thrust of the day, and the two sides seeking to stress the message that the deal being sought was the best one for both sides.
But, added Mr Barnier, the UK's decided to leave the EU and there will be consequences - "do not underestimate the consequences" - financial, social etc. He then says he will seek to try and take the emotion out of the process and try to minimise the consequences.
It is not about "punishment or revenge". But his warning of consequences makes for what feels like a less fraternal end to the news conference.
Michel Barnier says transparency is of great importance, particularly as Brexit is of huge interest to all 27 members.
"Everywhere I find great awareness of the responsibilities and issues at stake," he says.
David Davis agrees, saying he and the Prime Minister are of the same view and want to see the public informed - by proactive publication of what we are doing, not by leaks from cliques or erroneous briefings.
A journalist asks Mr Barnier "how confident" he is that he will still be dealing with Mr Davis in six months time given the fragility of the Tory government and its reliance on the Democratic Unionists for support.
"How flattering", the Brexit secretary jokes in response. He goes on to say that he hopes an agreement on residency rights can be struck reasonably quickly but that a settlement on issues relating to Ireland will take much longer.
However, he stresses that the UK's relationship with the DUP will not affect progress towards the latter in any what whatsoever.
As for Mr Barnier, he says he has known his counterpart for 20 years since they were EU British and French ministers respectively and that they got on well, adding that the UK is not the only country whose politics he follows closely.
In response to a question from the BBC's Europe editor Katya Adler, David Davis says nothing has changed in terms of the UK's approach to the single market and customs union from its pre-election blueprint.
In her Lancaster House speech earlier this year, Mrs May indicated that the UK would leave the single market and would seek separate but equivalent customs arrangements.
Mr Barnier echoes this, saying there are "different forms of co-operation" between EU members and third-party countries, adding that the UK "knows what the rules are for those kind of models".
ITV's James Mates asks about the sequencing of talks, noting how they seem to mirror the EU's proposals and says that they suggest a lack of leverage on the UK's part.
Mr Davis says what is important is "not how the talks start, but how they end".
He says that the UK wants talks on a future partnership with the EU to run in conjunction with issues relating to separation, adding that everything announced today is in keeping with what the UK set out in its letter activating Article 50 and the UK's position has not changed.
Other details coming out of a statement on the terms agreed for the talks show that the "principals" - those with overall responsibility for managing the negotiating process - "may decide to establish additional working groups, subgroups or organise breakout sessions".
The document also says each round of negotiations "should comprise public officials of both sides only".
Texts for discussion will have to be shared at least one week ahead fo talks.
We are on to journalist questions. Mr Davis is asked about the Irish border. He says that the issue took up more of the discussion than any other and that is why the two sides' top officials were tasked with overseeing it.
Mr Barnier rejects suggestions that the issue has been "set aside", saying it is highly "sensitive" and the EU is highly conscious of the political situation in Northern ireland and the change of political leadership in the Irish Republic.
All the commitments entered into in the Good Friday Agreement must be honoured and the Common Travel Area protected, he adds.
"We have an awful lot of work to do...so we come up with imaginative and concrete solutions," he adds.
A bit more of the detail coming through about the terms of the Brexit talks...
The negotiating rounds will "consist of plenary sessions and negotiating group meetings".
"Initial negotiating groups" have been set up focusing on citizens' rights, financial settlement and "other separation issues".
The statement goes on: "In addition, a dialogue on Ireland / Northern Ireland has been launched under the authority of the Coordinators".
The UK's Brexit Secretary says this is the first step of a long journey but the two sides have made a "promising start" - adding that substantive progress now needs to be made.
He says there is a long road ahead and then dusts off what he says is a quote of his own from Winston Churchill - a "pessimist sees the difficulty in every opportunity; an optimist sees the opportunity in every difficulty" - to prove he is a determined optimist.
It is David Davis's turn now. He starts by stressing how positive the talks have been. The timetable set out by the EU is "eminently achievable".
His goal is a strong and special partnership with the EU going forward.
On the key issue of the rights of EU citizens, he says the UK wants an agreement quickly and will set out "its offer" next Monday.
Details released by the EU show that the next stage of talks on Brexit will take place in the week beginning July 17.
The third round will be in the week beginning August 28; the fourth from September 18, while the fifth are set for the week beginning October 9.
Basically there's going to be one week of talks each month during the Brexit negotiating process.