"We made a good start last month but we are now getting into the substance of the matter", British Brexit Secretary David Davis told reporters as he was welcomed at the European Commission in Brussels by the EU negotiator Michel Barnier.
A picture of Mr Davis sitting opposite Mr Barnier as the negotiations got under way caused a bit of a stir, with the Brexit Secretary having no notes or papers in front of him.
The Chancellor, Phillip Hammond, accused his rivals in the Cabinet of trying to undermine his plans for a business-friendly withdrawal over the weekend.
One unnamed Cabinet minister was reported to have hit back, claiming Mr Hammond was part of an attempt by "the Establishment" to prevent Britain ever leaving the EU. Beyond these headline goals, they will discuss how to ensure a smooth transition on Brexit Day, a set of topics known as "other separation issues" where the ECJ looms large.
"For us it is incredibly important that we now make good progress, that we negotiate through this and identify the differences so that we can deal with them, and identify the similarities so we can reinforce them", Davis said.
More divisions were exposed last Sunday, when Hammond said transitional arrangements for Britain leaving the European Union are likely to last a couple of years, rather than the few months suggested by Trade Secretary Liam Fox.
Earlier on Sunday, Chancellor Philip Hammond had said senior British government ministers were becoming convinced of the need for transitional arrangements to reduce disruption as Britain leaves the EU. Barnier and Davis are to brief the media on Thursday, when they would give political endorsement to whatever officials have managed to agree.
Davis has warned May repeatedly that the uncertain fate of the citizens was souring his meetings with member-states, two people familiar with the matter told Bloomberg this month.
The negotiation is expected to be complicated, as May's minority government will face challenges at every step in the process.
They'll attempt to hammer out an agreement on what rights some 3.2 million European Union citizens in Britain and another million Britons living in the European Union will retain after Brexit.
Asides from the exit bill, the four-day negotiation will focus on citizens' rights and the border in Northern Ireland, among other issues. Unsurprisingly, the Brits have expressed opposition to these figures; Foreign Minister Boris Johnson labelled the sums "extortionate", saying Brussels can "go whistle" for the money.