A year after Britain voted to leave the bloc, the European Union's chief Brexit negotiator, Michael Barnier, and Britain's Brexit secretary, David Davis, have agreed on a two-year timetable for the negotiation of Britain's exit from the EU.
Both parties are hoping to make the divorce as clean as possible.
The EU's chief negotiator, Michel Barnier, says it's important that Britain withdraws from the union in an orderly way.
"Today we agreed on dates, we agreed on organisation and we agreed on priorities for the negotiation. In a first step, we will deal with the most pressing issues. We must leave the uncertainty caused by Brexit. We want to make sure that the withdrawal of UK happens in an orderly manner."
Britain's Brexit secretary, David Davis, also spoke after the first day of talks in Brussels.
Ireland has long been identified as a difficulty for the process, for identifying the rights of expatriate citizens and making decisions over a new EU-UK border.
The border between Northern Ireland and the Republic of Ireland will be the only land border between the EU and Britain once Brexit is complete in March 2019.
Mr Davis describes the issue as "technically difficult".
"I think Ireland has taken -- Northern Ireland and the Republic of Ireland -- have taken more time today than anything else. We discussed two aspects of it. One of course is the political sensitivities, which everybody understands, the other is the determination to maintain as near as possible an invisible border so we do not undermine the peace process, do not provide any cause for concern in Northern Ireland. This is a technically difficult issue."
British Prime Minister Theresa May has reaffirmed her commitment to a so-called "invisible border", essential given the number of people who would cross it every day.
"I'm personally committed to ensuring a practical solution that recognises the unique economic, social, cultural and political context of the land border with Ireland, which so many people pass through every day, and will remain our priority to work closely with the Irish government to ensure as friction-less and seamless border as possible."
Some doubt had been cast over the Brexit negotiations after the Conservative Party's terrible showing in the recent general election.
Theresa May called the election three years early in an attempt to increase the Conservatives' majority.
But the election returned a hung parliament, forcing the Prime Minister to try and form a coalition government with Ireland's Democratic Unionist Party (DUP).
Mr Davis says despite the political uncertainty, both Britain and the E-U are working towards "the best possible outcome".
"I have been encouraged by the constructive approach that both sides have taken. We've laid a solid foundation for future discussions with an ambitious but eminently achievable timetable. It was clear from the opening that both of us want to achieve the best possible outcome and the strongest possible partnership - one that works for the UK and for the EU."
But uncertainty surrounding the negotiations is presenting a risk to Britain's international capital market.
Managing director of the International Capital Market Association, Paul Richards, says the still-uncertain outcome of the negotiations poses a number of concerns.
"One of them is the shortage of time for the international capital markets to prepare for Brexit. Brexit is due to take place by March 2019, so there is a quite a short of time to prepare, and the markets do not yet know what the terms of the Brexit will be. Secondly, the markets want to know that they have legal certainty in their contracts over Brexit. Thirdly, they want to know that they're going to have continuing access to other markets, in particular when the UK leaves the European Union. And the terms of that access has yet to be negotiated. Then fourthly, they want to make sure that there are not different regulations in the UK from the European Union."
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