With the European Union agreeing to extend the deadline for Britain’s withdrawal from the bloc, the government remains in crisis, if with a bit more time to find a way forward. The old deadline of March 29 has now been pushed to at least April 12. Next week is certain to be tumultuous in Parliament.

Outside Parliament, companies are jumping ship. Fears of medicine shortages are rising. Prime Minister Theresa May has suffered two humiliating defeats over her withdrawal plan and the calls for her to resign are growing louder.

The government is now facing its biggest peacetime decision in decades. Almost every option remains on the table, from a daringly complete break with Europe to abandoning Brexit altogether.

What ultimately emerges could determine the shape of Britain and its place in the world for decades. Following is a basic guide to Brexit, what it is, how it developed into the mess it is today and how it could ultimately be resolved.

A portmanteau of the words “Britain” and “exit,” Brexit is shorthand for Britain’s split from the European Union, changing 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 1975, less than three years after it joined.) 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 it would offer were Remain and Leave, and Mr. Cameron was convinced that Remain would win handily.

On June 23, 2016, as a refugee crisis made migration a subject of political rage across Europe and among accusations of lies and fraudulent tactics on the Leave side, Britons voted for a hazily defined Brexit by 52 percent to 48 percent.

Not only did that not settle the debate, but it saved for another day the tangled question of what should come next. Now, that day may finally be arriving.

England and Wales voted for Brexit, overcoming support to remain in the European Union in London, Scotland and Northern Ireland. See a detailed map of the vote.

Europe is Britain’s most important export market and its biggest source of foreign investment, and being in the bloc has helped London cement its position as a global financial center. Every day, it seems, a major business announces or threatens plans to leave Britain after it quits the European Union, including Airbus, which employs 14,000 people and supports more than 100,000 other jobs.

The government expects the country’s economy to grow anywhere from 4 to 9 percent less than it would inside the bloc over the next 15 years, depending on how it leaves.

Mrs. May has promised that Brexit will end free movement, the right of people from elsewhere in Europe to move to Britain and vice versa. That is a triumph for some working-class people who saw immigration as a threat to their jobs, but dispiriting for young Britons hoping to study or work abroad.

Undoing 46 years of economic integration in one stroke was never going to be easy, and the Brexit process has been bedeviled by the same divisions that led to the referendum in the first place. Both Britain’s main parties, the governing Conservatives and the Labour opposition, are divided over what to do, leaving Parliament so factionalized that there may be no coherent plan most lawmakers would back.

Mrs. May spent 18 months negotiating a divorce deal with the European Union, shedding one cabinet minister after another in the process. But when she presented the plan to Parliament in January, it was rejected by a historic margin of 230 votes. When she tried again in March, she fared less badly, but the pact was still soundly defeated, 391 to 242.

The single greatest hangup is the question of Britain’s only land border with the European Union: the invisible line between Ireland, another member state of the bloc, and Northern Ireland, which remains part of the United Kingdom.

Mrs. May and her Irish counterpart, Leo Varadkar, want to keep checkpoints from going up at the border; that’s a crucial part of the Good Friday Agreement, which brought respite from decades of violence in Northern Ireland.

But the method she agreed for guaranteeing that — called “the backstop” — has alienated just about everyone.

The backstop would keep the whole United Kingdom in a temporary trading relationship with Europe until a final deal avoiding a hard border could be agreed, something that hard-line Brexiteers fear would never happen. And it would bind Northern Ireland to even more European rules, to the dismay of those who reject any regulatory differences between Northern Ireland and the rest of the United Kingdom. (They include the Democratic Unionist Party of Northern Ireland, whose 10 lawmakers give Mrs. May her parliamentary majority.)

Just about the only clear decision Britain has made on Brexit since the 2016 referendum was to give formal notice to quit under Article 50 of the European Union’s Lisbon Treaty, a legal process setting it on a two-year path to departure. That happened on March 28, 2017, which meant that this coming March 29 was initially set as the formal divorce date. Now that has been moved to April 12 — or May 22 if Parliament votes for Mrs. May’s deal next week, to give time to pass the other legislation it would require.

But Mrs. May and her government have yet to find a way to overcome seemingly impossible parliamentary arithmetic and get lawmakers to back her agreement with European leaders. The fantasy that Brexit would be easy is crumbling, and lawmakers who made lofty promises to their constituents are having to face the hard reality of a vote.

So far, Parliament has decisively knocked down Mrs. May’s deal, but also decided against removing her from power entirely. Mrs. May has yet to find a problem-free way forward. She could tack to the center by committing to a permanent trading relationship with Europe — a customs union — that would do away with tariffs and quotas. That way, she would solve the Irish border dilemma and possibly win some votes from opposition Labour lawmakers.

But that would also risk splitting her own Conservative Party, which she wants to avoid at all costs. So she has instead tried to win over right-wing lawmakers in her own party by acceding to their demand for measures that would risk anger in Brussels and a hard border in Ireland. Toward that end, she won some concessions from the European Union on the Irish border, but it has not been nearly enough to change the minds of a meaningful number of people in her own party.

Meanwhile, Jeremy Corbyn, the Labour leader, who has worked hard not to commit his party to a distinct course on Brexit, has expressed a willingness to back a second referendum under certain circumstances.

Mrs. May is now basically cornered. She wanted to bring her withdrawal plan for a third vote in Parliament, only to be unexpectedly denied by the House of Commons speaker, John Bercow.

Mr. Bercow, citing ancient precedent, said it would violate parliamentary rules to present the same legislation for another vote in the same parliamentary session, unless it had been substantially changed.

Mrs. May now hopes the extra time approved by the European Union will allow that third vote to happen (even if few analysts believe it will pass).

The other question is whether Parliament will finally take over the process. Earlier this month, lawmakers narrowly voted down an amendment that would have given Parliament the power to hold votes on other possible scenarios to find if there was a majority for a softer Brexit.

No one knows how things will turn out. Hard-line Brexiteers, who have been seeking a no-deal exit, may still come around to Mrs. May’s deal if they feel it is their only chance to achieve Brexit.

They fear that if nothing is approved by new April deadline, the government could be forced to seek a much longer extension on the withdrawal date – which could give backers of a second referendum time to build support for what currently seems a long-shot option. That could end in Britons reversing their decision to leave the European Union altogether.

There are other possibilities, too, like a general election that could put Mrs. May on more solid footing in Parliament — or lead to a government led by Mr. Corbyn that might negotiate a soft Brexit deal that would keep Britain closer to the bloc.

One thing is certain: It is a mess.