Mary Turner for The New York Times

After three years of haggling in the British Parliament, convulsions at the top of the government and pleas for Brussels to delay its exit, Britain closes the book on nearly half a century of close ties with Europe on Jan. 31.

Its split with the European Union was sealed when Prime Minister Boris Johnsons Conservative Party won a resounding victory in Decembers general election. That supplied Mr. Johnson with the parliamentary majority he needed to pass legislation in early January setting the terms of Britains departure, a goal that repeatedly eluded his predecessor, Theresa May. European lawmakers gave the plan their blessing later in the month.

Mr. Johnson, a brash proponent of withdrawal, will now guide the country through the most critical stage of Brexit: trade negotiations that will determine how closely linked Britain remains with the bloc.

Little will change overnight. At midnight in Brussels on Jan. 31 11 p.m. in London, a reminder that the European Union sets the terms of departure Britain will begin an 11-month transition in which it continues to abide by the blocs rules and regulations while deciding what sort of Brexit to pursue.

What ultimately emerges as Britain parts ways with the European Union could determine the shape of the nation and its place in the world for decades. What follows is a basic guide to Brexit: what it is, how it turned into a political mess and how it may ultimately be resolved.

Lets start with the basics

A portmanteau of the words Britain and exit, Brexit caught on as shorthand for the proposal that Britain split from the European Union and change its relationship to the bloc on trade, security and migration.

Britain has been debating the pros and cons of membership in a European community of nations almost from the moment the idea was broached. It held its first referendum on membership in what was then called the European Economic Community in 1975, less than three years after it joined. At the time, 67 percent of voters supported staying in the bloc.

But that was hardly the end of the debate.

In 2013, Prime Minister David Cameron promised a national referendum on European Union membership with the idea of settling the question once and for all. The options offered to voters were broad and vague Remain or Leave and Mr. Cameron was convinced that Remain would win handily.

That turned out to be a serious miscalculation.

As Britons went to the polls on June 23, 2016, a refugee crisis had made migration a subject of political rage across Europe. Meanwhile, the Leave campaign was hit with accusations that it had relied on lies and that it had broken election laws.

In the end, a withdrawal from the bloc, however ill-defined, emerged with the support of 52 percent of voters.

Brexit advocates had saved for another day the tangled question of what should come next. Even now that Britain has settled the terms of its departure, it remains unclear what sort of relationship with the European Union it wants for the future, a matter that could prove just as divisive as the debate over withdrawal.

How did the referendum vote break down?

Most voters in England and Wales supported Brexit, particularly in rural areas and smaller cities. That overcame majority support for remaining in the European Union among voters in London, Scotland and Northern Ireland. See a detailed map of the vote.

Young people overwhelmingly voted against leaving, while older voters supported it.

Why is it such a big deal?

Europe is Britains most important export market and its biggest source of foreign investment, while membership in the bloc has helped London cement its position as a global financial center.

With some regularity, major businesses have announced that they are leaving Britain because of Brexit, or have at least threatened to do so. The list of companies thinking about relocating includes Airbus, which employs 14,000 people and supports more than 100,000 other jobs.

The government has projected that in 15 years, the countrys economy would be 4 percent to 9 percent smaller if Britain left the European Union than if it remained, depending on how it leaves.

Mrs. May had promised that Brexit would mean an end to free movement that is, the right of people from elsewhere in Europe to live and work in Britain. Working-class people who see immigration as a threat to their jobs viewed that as a triumph. But an end to free movement would cut both ways, and the prospect was dispiriting for young Britons hoping to study or work abroad.

How did we end up with a Jan. 31 deadline?

Before Parliament approved Mr. Johnsons withdrawal agreement in January, just about the only clear decision it made on Brexit was to give formal notice in 2017 to quit, under Article 50 of the European Unions Lisbon Treaty, a legal process setting it on a two-year path to departure. That made March 29, 2019, the formal divorce date.

But departure was delayed when it became clear that hard-line pro-Brexit Conservative lawmakers would not accept Mrs. Mays withdrawal deal, which they said would trap Britain in the European market.

The European Union agreed to push the date back to April 12. But the new deadline did not bring about any more agreement in London, and Mrs. May was forced to plead yet again for more time. This time, European leaders insisted on a longer delay, and set Oct. 31 as the date.

Mr. Johnson took office in July, and vowed to take Britain out of the bloc by that deadline, with or without a deal. But opposition lawmakers and rebels in his own party seized control of the Brexit process, and moved to block a no-deal withdrawal, which would have meant Britain leaving without being able to cushion the blow of a sudden divorce.

That forced Mr. Johnson to seek an extension, something he had said he would rather be dead in a ditch than do. European leaders agreed to extend the deadline by three months, to Jan. 31, as Britain considered its options.

Ultimately, Mr. Johnson persuaded enough opposition lawmakers to agree to an early general election. His Conservative Party won an 80-seat majority, the largest since Margaret Thatcher in 1987.

What happens next?

Much as Jan. 31 marks a symbolic milestone, it is merely the beginning of a potentially more volatile chapter of the turbulent divorce, in which political and business leaders jockey over what sort of Brexit will come to pass.

Every path holds risks for Mr. Johnson, all the more so after an election in which he was buoyed by voters in ex-Labour heartland seats in northern and central England who stand to suffer from trading barriers with Europe.

And the clock is ticking: The end of the transition period is Dec. 31. Any request to extend that deadline would have to be made by June.

Mr. Johnson, though, has repeatedly vowed to complete the departure by the end of the year. If he sticks to his word, Britain and the European Union will have to strike a deal governing future trade across the English Channel at an unusually fast pace. (It took seven years, for example, for the European Union and Canada to negotiate their 2016 trade deal.)

That will involve negotiations over trade in manufactured goods as well as services, which make up the bulk of the British economy. Should the two sides fail to reach an agreement, even a narrow one that leaves some issues for next year, Britain would crash out of the bloc with no deal at all, raising the prospect of tariffs and border disruption that would mirror the sort of no-deal Brexit that lawmakers have long feared.

Among the points of contention will be Mr. Johnsons wish to break from European standards on labor, the environment and product safety. The more space Britain puts between its rules and Europes, the blocs leaders have said, the more they will hamper Britains access to the European market. Any restrictions of that sort would threaten British jobs, reliant as many of them are on European customers.

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What Is Brexit? And What Happens Next? - The New York Times