British and EU officials are negotiating day and night to get to the outline of a Brexit deal by Wednesday.
They need to resolve the final sticking points, notably on customs checks for Northern Ireland, before EU leaders meet to decide on next steps.
Here's what you need to know to understand an unprecedented divorce battle:
- Two agreements? -
The core of the talks so far have concerned arrangements for Britain's "orderly" separation from Europe after 40 years of shared trade and laws.
Often called the "divorce agreement", this text will take the form of a legal treaty and it must be agreed quickly to allow the British and EU parliaments to ratify it.
If it's not in place and ratified by March 29, Britain will crash out of Europe in a "no deal" Brexit with serious economic and legal consequences.
But there's also a second text.
The "political declaration" will be much shorter, maybe six or seven pages.
It will not be a legal text, but it could prove politically explosive.
The declaration will outline the parameters of future British relations with Europe, with goals like a free trade pact to be negotiated after Brexit day.
It won't be binding, but British lawmakers and voters may balk at paying tens of billions of euros in a divorce settlement with no detailed promises on future ties.
- Where are we now? -
EU negotiator Michel Barnier says the Brexit treaty is 80 to 85 percent ready. Irish Foreign Minister Simon Coveney went as high as 90 percent.
Both sides have agreed language on the rights of each others' citizens on their territory. They have put a number on the huge bill that Britain will pay.
A transition period has been agreed: Britain will apply EU rules and pay into the budget until 2020, while the future relationship is negotiated in more detail.
But you only get to 90 percent of a deal by leaving the hardest stuff until last.
Britain has not yet agreed that the European Court of Justice will have oversight if either side complains about the other breaking the treaty.
And the issue of Northern Ireland's borders could yet break the deal.
- The Irish problem? -
Both London and Brussels agree that there should be no return to border controls between Ireland and the British province of Northern Ireland.
Closer cross-border ties are a key development underpinning the return to peace since the Good Friday Agreement ended three decades of conflict.
Europe's preferred solution would be for Northern Ireland to remain in the EU Customs Union after Brexit, and for low-key controls between Britain and the North.
But Ulster unionists, including the small but influential DUP, will reject anything that divides them even symbolically from the core United Kingdom.
And hardline eurosceptic mainland politicians reject the alternative pushed by Prime Minister Theresa May, for all of Britain to remain in the customs union for now.
Europe -- while being ready to negotiate a trade deal after the divorce -- is wary of London trying to "cherry pick" single market access while rejecting EU rules.
- What's the answer? -
We will know by Wednesday whether May has decided to take up an invitation to outline any new plans to the other 27 EU leaders at a pre-summit dinner.
One idea that the British press has reported would be to extend the transition period beyond 2020, but it's not clear whether May's own party would back that.
Barnier, meanwhile, is insisting his border controls between Northern Ireland and the rest of the UK could be "de-dramatised" to the point of near invisibility.
If the negotiators can convince the EU leaders that a deal is imminent, they could call another summit next month to approve the package.
If they can't, the EU 27 will head back to their capitals to begin planning for a "hard Brexit".