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".
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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.
Quote Message: 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.