Later this month, Britain may do what no country has done before and vote to leave the European Union.

Opinion polls suggest the public is split down the middle. The referendum on June 23 is too close to call.

Those in favor of walking out of the EU -- the Brexit option -- say European rules stifle U.K. business and leaving would boost the economy. They also say Britain would regain control of its borders and be able to limit immigration.

Those campaigning for the U.K. to stay -- including the government -- paint a much grimmer picture of life outside the EU. They say trade and investment would suffer, triggering a recession, killing jobs, slamming the pound and causing house prices to fall.

The referendum is the biggest decision Brits have faced in a generation. The last direct vote on the country's ties with Europe was in 1975.

A win for Brexit would shape the future of the U.K. and Europe for decades to come. The big problem is that nobody knows exactly how.

Government crisis?

Prime Minister David Cameron would face huge pressure to resign. He is campaigning for Britain to stay in the bloc, but his Conservative party (and government) is bitterly divided over the issue.

Fellow Conservative and former London mayor Boris Johnson leads the Brexit campaign and may be a candidate to succeed Cameron.

Whoever leads the government, he or she would eventually have to give formal notice to the other 27 EU countries of the U.K.'s intention to quit.

There is no deadline for that to happen, but once it does there is no turning back. The U.K. would then have two years to negotiate its divorce from the EU -- including the terms of trade with its 440 million remaining consumers.

Read more: The truth about UK immigration

Economic turmoil?

The U.K. government, the International Monetary Fund, the Bank of England, Fed Reserve Chief Janet Yellen, President Obama and other world leaders have all warned that leaving the EU would hurt the U.K. economy -- the fifth biggest in the world.

They're worried about the impact on trade. By leaving, Britain would lose its automatic right to trade freely with the rest of the EU, which currently buys about 45% of British exports. The EU is an even bigger market for British services, such as banking and insurance.

On the other side, "Brexiteers" say the government could negotiate a new free trade agreement. But no country outside the EU has been able to secure that kind of privileged access to European markets without agreeing to pay into the EU budget or to accept free movement of citizens -- principles rejected by the Brexit campaign.

Investment and employment may also suffer. Many U.S. companies are heavily invested in Britain and use it as a gateway to the rest of Europe. So they may scale back in the U.K.

Other EU countries poured £496 billion ($708 billion) into Britain in 2014 -- almost half of all foreign investment. Those campaigning to remain in the EU say the flow of money could fall if the U.K. severs its links with the bloc. Many companies sell goods from their U.K. factories to other EU countries, and Brexit would make that harder.

A recent survey by professional services firm EY found that 72% of global companies see access to Europe as a key factor in deciding where to put their money. Nearly a third intended to either freeze or reduce their investment in the U.K. until the result of the referendum is known. Real estate investment has already been hit hard.

World leaders: Brexit is a 'serious risk to growth'

U.K. officials have said that up to 820,000 jobs could be lost if Britain leaves the EU. Several global companies have hinted they might shift jobs out of the U.K. The latest warning came from JPMorgan (JPM) last week.

Some Brexit campaigners have acknowledged that a vote to quit the EU could initially cost Britain jobs.

What happens to millions of migrants?

Migration is another hot topic. One of the core principles of the EU is the free movement of people, which gives citizens of any member state the right to live and work in any of the 28 countries in the union.

Those in favor of Brexit say leaving the bloc would allow the U.K. to decide which migrants to let in.

But an exit from the EU would raise questions about the status of roughly 3 million people from other EU states who currently live in the U.K. Campaigners say they would be allowed to stay, but future EU migrants would likely need a visa.

Brexit would also impact the roughly 1.2 million Brits living in other EU countries, as they could lose their right to travel around freely and access benefits such as healthcare.

Brexit: The big numbers you need to know

The domino effect?

A British vote to leave the EU could be the start of turbulent times for Europe. The EU is grappling with the world's worst refugee crisis in 70 years, and populist parties are gaining strength. The economy remains weak and unemployment high.

Support for the EU is falling sharply. A Pew Research Center study this week found that 47% of people in 10 member countries have an unfavorable opinion of the EU.

EU leaders are worried that if Britain decides to leave, other countries could follow. That could lead to a gradual unraveling of the EU, with huge consequences for the global economy, security and stability.

A more immediate threat is the risk that the United Kingdom could break apart. Leaders of the Scottish National Party have said they would seek a new referendum on Scotland's independence if Britain votes to leave the EU.

Scots are expected to vote in favor of keeping the U.K. in the EU.