Britain announced on Monday that it will begin the process of leaving the European Union via a formal letter to EU President Donald Tusk on March 29.
Here is an outline of what we know:
- Timing -
Britons voted by 52 percent to 48 percent to leave the EU in a referendum in June 2016.
May will trigger Article 50 of the EU's Lisbon Treaty, which begins the two-year withdrawal process, on March 29.
The EU has said it will issue its first plan for Brexit talks within 48 hours, before finalising its strategy at a summit set to take place between four and six weeks after Article 50 is triggered.
But formal talks between London and Brussels are not expected to start for six to eight weeks, according to EU sources, and possibly later while waiting for the result of German elections in September.
The European Commission's Brexit negotiator Michel Barnier has said they must be wrapped up by October 2018 to give the EU and national parliaments time to ratify the deal.
- Priorities -
May will prioritise controlling immigration from the rest of the bloc, after the issue dominated the referendum campaign.
She acknowledges this will mean leaving Europe's single market, of which freedom of movement is a key principle, and likely also the customs union.
Britain believes it can negotiate the exit agreement and a deal on future relations within the two-year negotiating period, although diplomats are sceptical.
Some in the EU argue that the divorce must be finalised first -- including the contentious issue of Britain's outstanding bills, which EU officials have estimated at 60 billion euros.
European leaders have also been clear that Britain cannot get a better deal outside the EU than it had inside, amid fears that Brexit could cause other nations to leave the bloc.
Both sides would like the early resolution of the status of more than three million Europeans living in Britain, and more than one million Britons living elsewhere in the EU.
- Trade -
Amid fears of the impact on jobs and growth of leaving the single market, May is pushing for "maximum possible access" for British companies.
The government has indicated that Britain could make contributions to the EU budget to ensure trade access.
Continued full membership of the customs union is unlikely as it would prevent Britain striking its own trade deals with non-EU countries, a key plank of May's strategy for a new "global Britain".
May suggested Britain could sign up to some aspects of the customs union.
The prime minister also says she wants a "phased period of implementation" of a new relationship with the EU to give businesses time to plan.
She has said she wants a new relationship that is good for Britain and the EU, but would rather walk away than accept a bad deal.
Without a new trade agreement, Britain would fall back on World Trade Organization (WTO) rules, which could mean higher export tariffs and other barriers.
- Immigration -
Hundreds of thousands of Europeans, mainly from eastern and southern member states, move to Britain each year and May is committed to radically reducing this.
Brexit minister David Davis has said there would be no sudden drop in numbers, as it would take years to fill low-skilled jobs in hospitality, social care and agriculture currently done by immigrants.
- Security -
May has promised Britain will remain a "reliable ally" to the EU and wants "practical arrangements" on law enforcement and intelligence cooperation.
She has also stressed Britain's commitment to defending European security through NATO.
- Parliament -
The Supreme Court ruled in January that May's government must obtain approval from the British parliament to trigger Article 50, prompting the introduction of emergency legislation.
The House of Lords put up some opposition, but support in the elected House of Commons meant the bill passed unamended.
May has promised parliament a vote on the final Brexit deal, but warned that rejecting it meant Britain would leave without any agreement.
Other battles lie ahead, particularly over the Great Repeal Bill.
The bill to be introduced later this year will serve the dual purpose of repealing the European Communities Act and incorporate more than four decades of EU law into British law.
MPs would then decide which laws to reject, adopt or amend.
May's Conservatives have a slim working majority of 17 in the Commons, and have a large lead over the deeply divided Labour party in opinion polls.