It's essentially a choice of a harder or softer Brexit. Harder prioritizes border control over trade. UK firms would pay tariffs to do business in the EU, and vice versa. The softest Brexit would see access to the single market, or at least a customs union, maintained. That would require concessions — including the payment of a hefty "divorce bill" — to which the UK has provisionally agreed.

Businesses have expressed concern about a "cliff edge" scenario, where Britain leaves the EU with no deal. Even if an agreement is reached at the EU bloc level, the worry is that it could be rejected at the last minute. Each of the 27 remaining countries must ratify the arrangements, and any might reject them. That could mean chaos for businesses and individuals.

If there is no agreement at all, a fully sovereign UK would be free to strike new trade deals and need not make concessions on the rights of EU citizens living in the UK or pay the financial settlement of outstanding liabilities. However, trade would be crippled. UK citizens in other parts of the EU would be at the mercy of host governments. There would also be a hard EU-UK border in Ireland.

The EU and the UK could reach a deal on Britain's exiting the bloc without an agreement on future relations. This scenario would still be a very hard Brexit, but would at least demonstrate a degree of mutual understanding. Trade agreements would be conducted, on an interim basis, on World Trade Organization rules.

Most trade tariffs on exported goods are lifted, except for "sensitive" food items like eggs and poultry. However, exporters would have to show their products are genuinely "made in Britain" so the UK does not become a "back door" for global goods to enter the EU. Services could be hit more. The City of London would lose access to the passporting system its lucrative financial business relies on.

Under the Swiss model, the UK would have single market access for goods and services while retaining most aspects of national sovereignty. Switzerland, unlike other members of the European Free Trade Area (EFTA), did not join the European Economic Area (EEA) and was not automatically obliged to adopt freedom of movement. Under a bilateral deal, it agreed to do so but is still dragging its feet.

As part of the European Economic Area, Norway has accepted freedom of movement – something that no Brexit-supporting UK government would be likely to do. Norway still has to obey many EU rules and is obliged to make a financial contribution to the bloc while having no voting rights. Some see this as the worst of both worlds.

Turkey is the only major country to have a customs union with the EU, as part of a bilateral agreement. Under such an arrangement, the UK would not be allowed to negotiate trade deals outside the EU, instead having the bloc negotiate on its behalf. Many Brexiteers would be unwilling to accept this. It would, however, help minimize disruption at ports and, crucially, at the Irish border.

May became prime minister after David Cameron resigned from the post in the wake of the Brexit referendum vote in June 2016. Despite her position, she has struggled to define what kind of Brexit her government wants. Hardliners within her Conservative party want her to push for a clean break. Others want Britain to stay close to the bloc. The EU itself has rejected many of May's Brexit demands.

The leader of the British Labour Party has no formal role in the Brexit talks, but he is influential as the head of the main opposition party. Labour has tried to pressure the Conservative government, which has a thin majority in Parliament, to seek a "softer" Brexit. But Corbyn's own advocacy has been lukewarm. The long-time leftist voted for the UK to leave the European Community (EC) in 1975.

Boris Johnson's turbulent two years as UK foreign secretary came to an abrupt end with his resignation on July 9. The conservative had been a key face for the Leave campaign during the 2016 referendum campaign. Johnson disapproves of the "soft Brexit" sought by PM May, arguing that a complete break from the EU might be preferable. He became the second Cabinet member within 24 hours to quit...

David Davis headed Britain's Department for Exiting the EU and was the country's chief negotiator in the talks before he quit on July 8, less than 24 hours before Downing Street announced Boris Johnson's departure. Davis had long opposed Britain's EU membership and was picked for the role for this reason. Davis was involved in several negotiating rounds with his EU counterpart, Michel Barnier.

Raab replaced Davis in early July 2018. But he only lasted four months, resigning a day after Theresa May presented a draft withdrawal plan to her cabinet. Raab previously worked for a Palestinian negotiator in the Oslo peace process and as an international lawyer in Brussels advising on European Union and World Trade Organization law.

Jeremy Hunt was Britain's Health Secretary until he replaced Boris Johnson as foreign secretary in early July 2018. The 51-year-old supported Britain remaining in the European Union during the 2016 referendum, but said in late 2017 that he had changed his mind in response to the "the arrogance of the EU Commission" during Brexit talks. He has vowed to help get Britain a "great Brexit deal."

Nigel Farage was the leader of the United Kingdom Independence Party (UKIP) until July 2016. Under his stewardship, the party helped pressure former Prime Minister David Cameron into calling the EU referendum. He was also a prominent activist in the Leave campaign in the lead-up to the vote. Farage still has some influence over Brexit talks due to his popularity with pro-Leave voters.

Businessman Arron Banks is a friend of Nigel Farage, and donated a significant sum to the former UKIP leader's Leave.EU campaign – making him the group's biggest financial backer. He had several meetings with Russian officials ahead of the referendum, but has denied allegations of collusion with Moscow in the Brexit vote, branding the claims a "political witch hunt."

EU Commission President Juncker (left) and EU Council President Tusk (right) share two of the bloc's highest posts. Juncker heads the EU's executive. Tusk represents the governments of the 27 EU countries — the "EU 27." Both help formulate the EU's position in Brexit negotiations. What Tusk says is particularly noteworthy: His EU 27 masters — not the EU commission — must agree to any Brexit deal.

The former French foreign minister and European commissioner has become a household name across the EU since his appointment as the bloc's chief Brexit negotiator in October 2016. Despite his prominence, Barnier has limited room to maneuver. He is tasked with following the EU 27's strict guidelines and must regularly report back to them during the negotiations.

The Irish PM has been one of the most important EU 27 leaders in Brexit talks. Britain has said it will leave the EU's customs union and single market. That could force the Republic of Ireland, an EU member, to put up customs checks along the border with Northern Ireland, a British province. But Varadkar's government has repeatedly said the return of a "hard" border is unacceptable.

The leaders of the EU 27 governments have primarily set the EU's negotiating position. They have agreed to the negotiating guidelines for chief negotiator Barnier and have helped craft the common EU position for Tusk and Juncker to stick to. The individual EU 27 governments can also influence the shape of any Brexit outcome because they must unanimously agree to a final deal.