Chief U.K. negotiator David Davis is meeting his European Union counterpart, former French foreign minister Michel Barnier, to grapple with a complex set of questions about the future of trade and migration, how much the country must pay to settle its bill with the bloc, and the rights of millions of citizens who have settled in Britain or Europe.
Formal talks to agree a host of issues around the terms of the UK's departure from the bloc will begin on Monday, nearly a year to the day after the referendum vote to leave.
While Britain has struggled to agree on and present a coherent list of demands, the 27 European Union nations have had one message all along - in the words of Barnier on Monday: "We must first tackle the uncertainties caused by Brexit".
"Today we agreed on dates, we agreed on organization, and we agreed on priorities for the negotiation", he said, outlining a two-step negotiation.
Mr Davis went into the talks announcing that he was in a "positive and constructive" frame of mind and that he was determined to build a "strong and special partnership" with the EU.
Barnier said there will be one week of negotiations every month and the two sides will use the time in between to work out proposals. Perhaps more important, they begin just 10 days after a humbling election setback revived divisions within May's government on what kind of relationship it wants with the EU.
Hammond signalled that he was in favour of an extended transitional arrangement, to help the United Kingdom avoid the "cliff edge" Brexit which most economists agree would be hugely damaging to the country's economy. In a tweet on Sunday afternoon, he said: "Back this weekend in my countryside, Savoie, to draw the strength and energy that the long hike requires".
The Commission said: "The opening of negotiations at political level will focus on issues related to citizens' rights, the financial settlement, the Northern Irish border and other separation issues, as part of the sequences approached to talks".
May herself will also have a chance to update the other 27 European Union leaders on her Brexit plans at a summit meeting in Brussels on Thursday.
Prime Minister Theresa May has repeatedly insisted the Government is prepared to walk away from the talks, claiming no deal is better than a bad deal.
While the European Union is insisting on securing divorce terms first, the U.K.is still pushing for simultaneous discussions on a future relationship to be anchored by a sweeping free-trade accord.
The EU has also argued that the withdrawal deal would need the oversight of the European Court of Justice (ECJ) in order to be enforced, and to have the ability to sort out any possible disputes in future.
Today's talks are expected to be the first of four or five sets of talks to be held over the summer concerning the first phase of the negotiations, namely the terms of Britain's departure from the EU.
Threats by Britain to walk away without a deal have also anxious European capitals.
May's chancellor Philip Hammond became the first distanced himself from May's hardline position yesterday, saying that crashing out of the European Union without a deal would be "very, very bad" for Britain.