Brexit: What are the options?
Theresa May is due to set out more details of her approach to the UK's departure from the EU.
Tuesday's speech could be a big moment in finding out what the UK's relationship with the European Union will look like after Brexit.
Some other countries already have their own arrangements, governing how they trade with the EU:
|Alternative Brexit models|
|Single market member?||Full||Full||Partial||No||No||No|
|Tariffs?||None||None||None||Reduced tariffs through free trade deal||None on industrial goods||Yes|
|Accept free movement?||Yes||Yes||Yes||No||No||No|
|In the customs union||Yes||No||No||No||Yes||No|
|Makes EU budget contributions||Yes||Yes||Yes (but smaller than Norway)||No||No||No|
But what does all this mean? Here's a guide to some of the terms and key debates that we're likely to be be hearing about.
Hard Brexit or soft Brexit?
There is no strict definition of either, but they are used to refer to the closeness of the UK's relationship with the EU, post-Brexit.
So at one extreme, "hard" (or "clean") Brexit could involve the UK refusing to compromise on issues like the free movement of people, leaving the EU single market and trading with the EU as if it were any other country outside Europe, based on World Trade Organization rules.
This would mean - at least in the short term before a trade deal was done - the UK and EU would probably apply tariffs and other trade restrictions on each other.
At the other end of the scale, a "soft" Brexit might involve some form of membership of the European Union single market, in return for a degree of free movement.
Norway-style, Canada, or neither?
A number of non-EU countries have their own relationships with Brussels, with differing degrees of closeness, which could give an idea of what is to come for the UK.
Norway, for example, has full access to the single market, but is obliged to make a financial contribution and accept the majority of EU laws, and all EU citizens can move to live and work there, under free movement laws.
Given that Downing Street has said any deal must involve controls on immigration, it seems unlikely that the UK will accept free movement as it currently applies.
Another example is Canada - which has agreed a new trade deal including preferential access to the single market without all the obligations that Norway and Switzerland - whose access to the EU market is governed by a series of bilateral agreements - face.
However, while post-Brexit Britain may contain elements of these arrangements, Mrs May has stressed the UK does not want an "off the shelf" deal.
Access or member?
"Access to" and "membership of" the single market are sometimes used interchangeably but they mean very different things.
All 28 EU countries are full members of the single market which enables them to trade with one another based on the four freedoms of the EU: free movement of goods, services, capital, and people.
The European Economic Area (EEA) on the other hand is the name of the open internal market between the EU and Norway, Iceland, and Liechtenstein.
The EEA agreement grants these three countries near-full access to the European single market. In return, they are subject to obligations from EU legislation in relevant areas and have to accept free movement of people.
Chancellor Philip Hammond has said if the UK is "closed off" in trade terms by the rest of the EU, it could be forced into adopting a "new economic model", comments interpreted as suggesting cuts to corporation tax to allow the UK to entice business from elsewhere in Europe.
Work permits or visa waivers?
The government says immigration curbs will be an essential part of the Brexit package but how they will work is not yet clear.
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.
A combination of different models is also an option, and the government says all possibilities are being considered.
It has also been reported a visa waiver scheme, similar to that used by the US, could apply to Britons going to the EU.
This could involve an online application and paying a fee in order to visit the EU, without requiring a full visa.
What's a customs union?
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.
But you do not have to be a member state to be in a customs union with the EU.
After Brexit, the UK could adopt a similar model to Turkey, which is not an EU member but trades with the EU as part of a customs union.
However, this would be unpopular in some quarters as by agreeing to set common external tariffs, customs unions also limit the freedom of their individual members to strike their own trade deals.
Just like with the referendum itself, opinions differ on what the government should do next. Some in the Conservative Party want a fast "hard" Brexit, while others - including many of the leading Remain campaigners - say access to the single market should now be the priority.
Some Leave campaigners like Conservative MP John Redwood say Brexit is a sovereign decision that should be completed as quickly as possible.
He wrote that the UK should "offer to continue tariff-free trade, send them the letter and then leave".
Other Conservatives have urged the PM to take her time to strike a deal.
Labour leader Jeremy Corbyn says the UK needs to "maintain full access" to the EU single market in order to protect jobs.
EU leaders' warnings
Several EU leaders have called for clarity on what the UK wants from the Brexit negotiations.
The EU's chief negotiator, Michel Barnier, is among those to tell the UK it cannot "cherry pick" on issues such as the single market.
Several have stressed that for the UK to enjoy continued free access to the single market, it would need to accept free movement of people.
We will know more about the EU's position once formal negotiations begin, which will happen when the UK serves notice of its departure under Article 50 of the Lisbon Treaty, which Mrs May has promised to do before the end of March.
There has been much talk of an interim deal between the UK and the EU before the final terms are agreed.
Supporters of the plan say it would avoid the "cliff edge" scenario which could see tariffs imposed on businesses as soon as the UK leaves the EU, and prevent a shock to the economy.
Not everyone is convinced this is necessary - and some Conservative MPs want the UK to leave the EU before negotiating the terms.
But a transitional arrangement appeared to get more likely after Chancellor Philip Hammond said there was an "emerging view" that having longer than two years to negotiate the UK's departure would tend towards a "smoother transition" .
Writing in the Sunday Times, Brexit Secretary David Davis suggested there might be a transitional arrangement to ensure Britain's exit was a smooth process.
A hint of what the UK might be looking for - and a suggestion of how tricky the negotiations might be - was offered by Oliver Letwin, who was briefly in charge of the government's Brexit unit before Theresa May took over as prime minister.
Speaking on the BBC's Daily Politics, he compared what he thought was the UK's likely wish list to having "cake and eating it".
The former Conservative minister said this should include access to financial services for the City of London, a zero tariff regime for the import and export of goods - as well as control over immigration.
The cake theme re-emerged when notes carried by an MP's aide were photographed in Westminster.
The handwritten notes included the phrase "what's the model? Have your cake and eat it" and "unlikely" in reference to the EU single market.
Downing Street said this did not reflect its Brexit position.