Brexit at-a-glance: What we learned from Theresa May
With her Brexit speech, Theresa May has for the first time revealed some key details about her approach to negotiations with the EU.
Here's what we know now:
Leaving the single market
What it is: The single market aims to make it easy for EU nations to trade with one another. It allows free movement of goods, workers, services and capital around the EU, without any tariffs, pretty much as if it was all one country. While it remains in the EU, the UK is a full member of the single market, and much of the Brexit debate has been about what will happen when it leaves. Some non-EU countries - such as Norway - have arrangements with the EU that allow them to be part of the single market if they meet certain conditions.
UK government position: Having previously not publicly committed either way, Theresa May confirmed the UK cannot remain a member of the single market after it leaves the EU.
She said this was because, as European leaders have stressed, the UK would have to accept EU rules and regulations and be bound by the European Court of Justice.
Instead, she said, the UK will push for a new "comprehensive free trade agreement", giving it "the greatest possible access" to the single market.
The deal might contain "elements" of the current arrangements, she said, singling out the the motor trade and financial services as examples.
Seeking a new customs union deal
What it is: A customs union is an arrangement between countries who agree not to impose tariffs on each other's goods. They also agree to impose common external tariffs on goods from countries outside their customs union. Setting common external tariffs is what distinguishes a customs union from a free trade area, where members are able to set their own tariffs on goods from the rest of the world. As an EU member, the UK is currently part of its customs union.
What we know: The PM specified that the UK will leave the EU customs union, saying elements of it (the Common Commercial Policy and the Common External Tariff) prevented the UK from striking trade deals around the world.
At the same time, she said she wanted the UK "to have a customs union agreement with the EU".
She added: "Whether that means we must reach a completely new customs agreement, become an associate member of the customs union in some way, or remain a signatory to some elements of it, I hold no preconceived position."
The 28 member states are in the EU customs union, but the EU also has separate customs union agreements - which vary in scope, for example in relation to the type of goods covered, with a number of other countries.
New EU migration powers
The government has made clear that there will be restrictions to EU migration as a result of the referendum.
This was reiterated by Mrs May in her speech, saying: "The message from the public before and during the referendum campaign was clear: Brexit must mean control of the number of people who come to Britain from Europe. And that is what we will deliver."
But the precise model to be used has not yet been confirmed.
During the referendum campaign, Vote Leave called for a "points-based" system, similar to that used in Australia.
But this model, which would involve applications being accepted on the basis of skills, has been rejected by Mrs May, who says it would not give sufficient control to the government.
An alternative, which Home Secretary Amber Rudd has said is under consideration, is to require migrants to have a work permit before coming to work in the UK, with ministers able to prioritise different sectors.
The government has said all possibilities are being considered.
What about expats?
The fate of EU citizens currently living in the UK and of UK citizens living in the rest of the EU has become another pressing question.
The government has repeatedly stated that the UK could not make commitments on the right of EU citizens to remain in the UK without securing a reciprocal deal for British citizens living abroad in Europe.
"I have said on many occasions that I expect to be able to, and wish to be able to, guarantee their status here in the UK, but we do need reciprocity - we need to have care and concern for UK citizens who are living in the European Union," Mrs May told MPs last month.
In her speech, she said many countries wanted a deal, but "one or two others do not", and called for a resolution as soon as possible.
MPs will get a vote on the deal
Mrs May confirmed: "l will put the final deal that is agreed between the UK and the EU to a vote in both Houses of Parliament, before it comes into force."
After her speech, Brexit Secretary David Davis told MPs the UK would be leaving the EU whatever the outcome of the vote.
The government will also be forced to consult Parliament before starting negotiations if it loses the legal challenge over Article 50 of the Lisbon Treaty.
Not bound by the European Court of Justice
The prime minister has been clear the UK will no longer be bound by the Luxembourg-based European Court of Justice, which ensures the application of EU legislation, after Brexit.
"We are not leaving only to return to the jurisdiction of the European Court of Justice," she told the Conservative Party conference.
"That's not going to happen."
Deal to be 'phased in'
There has been much talk of an interim deal between the UK and the EU before the final terms are agreed.
But different versions of what this could mean have been put forward.
In her speech, Mrs May said there would be no "unlimited transitional status", which would leave the UK in "some kind of permanent political purgatory".
However, she proposed a "phased process of implementation" after a deal has been reached, to allow each element of the deal to be introduced.
Contribution to EU budgets
As it will not be in the single market, the UK will not pay "huge sums" to EU budgets, Theresa May said.
In some circumstances it may have to make an "appropriate contribution" to be part of European schemes, she said.
"But the principle is clear: the days of Britain making vast contributions to the European Union every year will end."
'No deal better than a bad deal'
The PM gave her strongest warning yet to her opposite numbers ahead of the negotiations, saying a "punitive deal that punishes Britain" would be "an act of calamitous self-harm for the countries of Europe" and would "not be the act of a friend".
She added that "no deal for Britain is better than a bad deal for Britain".
There was another warning for the EU in the PM's speech, as she told leaders to "respect difference", rather than "trying to hold things together by force, tightening a vice-like grip that ends up crushing into tiny pieces the very things you want to protect".
The government had already set itself a Brexit deadline - Theresa May will give notice of the UK's departure from the EU under Article 50 of the Lisbon Treaty before the end of March.
This allows two years for the negotiations to be completed before the UK leaves. The government has insisted neither a pending Supreme Court judgement nor the political upheaval in Northern Ireland will delay its timetable.
What will happen to EU funding currently given to projects and different regions across the UK?
We know that during negotiations with the EU, all rights and obligations from EU membership will continue as normal. This means that the UK will continue to contribute to the EU budget and that all projects in the UK that currently benefit from EU funding will continue to do so while the UK remains a member of the EU.
In August, the Treasury said it would guarantee to back EU-funded projects signed before the Autumn Statement (23 November).
Agricultural funding now provided by the EU will also continue until 2020.
In October, Chancellor Philip Hammond told the Conservative Party conference the Treasury would guarantee payments for multi-year EU funding secured before Brexit after Britain left the EU.