Image source, Reuters

Speaking to reporters ahead of the summit, Luxembourg PM Xavier Bettel says he would favour an "intelligent extension".

He denies he is losing patience with the UK, but says waiting for British politicians to come to a decision is like the Samuel Beckett play Waiting for Godot.

Famously, the title character in that production never arrives.

He says that the UK should have to make preparations to take part in May's European Parliament elections, adding: “no elections, no extension”.

Here's a clip of the exchange before the summit discussions began - which reportedly turned out to be sparked by a photograph showing Theresa May and Angela Merkel addressing their respective parliaments earlier today in the same colour of jacket.

Image source, Reuters

As the EU leaders discussions continue, the BBC's Christian Fraser in Brussels says there are reports of a disagreement between the French and German leaders at the summit as to the length of the Brexit extension they would be prepared to allow.

Reuters, quoting a French presidency official, say the current Brexit documents do not include "serious guarantees", and therefore the UK should not be allowed a long extension.

Meanwhile, some details have begun to emerge from Theresa May's address to fellow EU leaders.

Reuters says the prime minister signalled she was open to accepting a longer Brexit delay, so long as it could be cut short.

And EU officials are describing her performance as "more solid than usual".

They say she spoke for just over an hour before leaving the room to let them decide on the length of a Brexit extension and on whether they would attach conditions.

However, the officials also say Mrs May still lacked "many specifics", adding "leaders have many questions."

BBC News Channel

BBC political correspondent Alex Forsyth says it appears Theresa May learned lessons from the last EU summit when "she took a bit of a grilling from EU leaders and they weren't overly impressed with all of her performance".

"Today, Theresa May, knowing what is at stake for her now - both in Brussels but also in Westminster - has taken steps to try and get round as many EU leaders as possible, having diplomatic sessions before she went...

"The sense we are getting is that things went a little bit better around the table this evening".

Our political correspondent adds Mrs May "very deliberately" tried to approach this summit in the "most constructive way she can".

Adam Fleming
Brussels reporter

EU leaders are considering updated draft conclusions on the PM's request for a Brexit delay.

One paragraph of the draft has been changed to specify what role the UK will be able to play in the EU's decision-making processes.

Another part of the document has been expanded to make clear that the other EU countries can meet without the UK at all levels to consider post-Brexit issues.

The date is still XX.XX.XXXX - an indication no agreement has been reached on the length of any extension just yet.

Earlier we brought you a picture of German Chancellor Angela Merkel showing Theresa May something funny on a tablet.

We didn't know what the leaders were joking about, but now we have an answer, courtesy of the BBC's political editor...

BBC News Channel

German MEP Gabriele Zimmer says she sees it as a "problem" to try and predict what will happen this evening.

She believes it is not possible find a solution at the moment which doesn't involve the UK taking part in European elections.

"I would like to welcome the British members to the European parliament," but it makes "no sense" to have them leave after two months after the Parliament is formed, she says.

Conservative MP Damian Green says that electing British MEPs would be "madness".

The former cabinet minister says he hopes that the Conservative and Labour can agree a cross-party solution, which would avoid the need to hold European Parliament elections next month.

"It is conceivable" that the UK could see changes to the backstop in order to allow the withdrawal agreement to pass, he says.

"It is not at all sensible to do" a leadership election for the Conservative Party now, he says.

Chris Morris
BBC Reality Check

Ahead of the summit, president of the European Council, Donald Tusk, urged European Union leaders not to humiliate Theresa May when they discuss her latest request to delay Brexit.

But the other 27 EU countries may still impose tough conditions on any extension to the Article 50 negotiating period, to ensure that they protect their own interests.

As the summit begins, BBC Reality Check correspondent Chris Morris assesses what's at stake.

German Chancellor Angela Merkel appeared to be breaking the ice ahead of the first part of tonight's summit by showing fellow leaders something funny on a tablet.

Theresa May and Luxembourg's Xavier Bettel appeared to be in on the joke, as was European Council President Donald Tusk.

On the right, it looks like Portugal's Antonio Costa wanted in as well...

Image source, AFP

Image source, EBS

Speaking to reporters earlier, the President of the European Parliament, Antonio Tajani, said the "most important thing" is to defend the rights of European citizens in the UK and UK citizens in Europe.

"We want to know the UK decision, and then we need to decide in the council."

Image source, Getty Images

Theresa May has started her meetings.

Her first discussion is with European Parliament President Antonio Tajani.

The PM will then brief the 27 EU leaders and take questions, before leaving the room, leaving them to discuss her request to extend Article 50.

BBC News Channel

Sophie Pedder, Paris Bureau Chief for the Economist believes Emmanuel Macron "has somewhat changed his tone", having originally taken the "hardest line" against the UK.

"He's more open to the idea of an extension of some sort," she says, but "with conditions" that the UK will guarantee to work co-operatively with the EU.

He doesn't want the UK to be in the EU in a "wrecking position" Ms Pedder tells the BBC.

Image source, Reuters

Also arriving ahead of the summit was the EU's chief Brexit negotiator Michel Barnier, who told reporters any Brexit delay must be "useful" and "serve a purpose".

"Our common purpose is to get the ratification of the withdrawal agreement", he says.

"Let me recall that this withdrawal agreement is the only way to ensure an orderly withdrawal of the UK, which is our common interest."

"So now it is for the leaders to decide tonight."