The European Commission has said that "sufficient progress" must be made on three key issues before it will move on to negotiations on trade and the transition to a future EU/UK relationship.
Here are the three "divorce issues" and the obstacles believed still to stand in the way of a breakthrough:
The question of the post-Brexit rights of three million EU citizens living in the UK and more than one million Britons living on the continent has been central to negotiations so far. Both sides insist they want to protect individuals' rights on issues like residence, welfare benefits and access to healthcare. But differences remain over the EU's demand for the European Court of Justice to retain jurisdiction over cases involving EU citizens in the UK.
There has been no official confirmation of reports suggesting Theresa May could seek to break the deadlock by offering the UK Supreme Court the power to refer cases up to the ECJ if it felt itself unqualified to judge on them.
The financial settlement
Unofficial briefings suggest the UK has accepted a formula which would see it pay around 45-55 billion euro (£40-49bn) over a number of years to settle liabilities entered into while a member of the EU. These include future funding for projects agreed by the UK, invoices which have not yet been settled from the EU's multi-year budget, outstanding loans to non-EU countries and pensions for EU staff who worked for the institutions during the UK's membership.
Despite the earlier suggestion of pro-Brexit minister Boris Johnson that the EU could "go whistle" for any excessive payment, is not thought that any disagreement remains about the way the "divorce bill" will be calculated. Its precise size may not be known for many years.
The Irish border
The status of the border between Northern Ireland and the Republic has risen up the agenda in recent weeks to become the major stumbling block in the way of agreement. Both sides insist they want an open border with no checkpoints or guards, but no format for achieving this has yet been devised which satisfies all interested parties.
Brussels is concerned that the adoption by Northern Ireland of different regulations on issues like food safety, environmental health and workers' rights would make border checks necessary, in order to prevent goods which do not meet EU standards being brought into the bloc, potentially undercutting European rivals. But the Democratic Unionist Party - and many Conservatives - reject any outcome which sees Northern Ireland treated differently from the rest of the UK.