The negotiations will be tough and complex, covering everything from fishing and farming to trade and migrants across a continent.
While covering such topics, Theresa May has to balance the needs of both Leavers and Remainers - still with stubbornly large gulfs in opinion between the two groups - when striking a deal for a new relationship with Europe.
May needs to be seen to cut migration
Immigration was a driving force for the Leave vote in the UK, with key Brexiters promising that the country would have control over the number of people coming in.
2016 was the first time net migration to the UK from the EU exceeded that from the rest of the world combined, with both levels falling. Net migration in the year to September stood at 165,000 from EU countries - compared to 164,000 from all the other countries.
Despite the economic consequences of lower migration, this level is expected to fall further. The Office for National Statistics is assuming a fall in net migration, from 300,000 a year to under 200,000 from 2020.
While also pledging to restore sovereignty
Sovereignty was a key issue in the EU referendum campaign, and Theresa May has vowed that Britain will regain control over its laws.
Currently, the UK's laws are decided by British institutions such as Parliament, as well as the European Union - in the form of the European Commission (the EU's administrative arm), the European Parliament (representing EU citizens) and the Council of Ministers (representing member states).
While number are impossible to obtain, Professor Chalmers has previously estimated that 14 to 17 per cent of UK law is derived from our EU membership.
But according to Sara Hagemann of UK in a Changing Europe, even though the UK votes against the majority in the EU Council more frequently than other member states, it is incorrect to say that the UK consistently loses in the EU.
Since 1999, when decision records became available from the EU Council where governments meet to negotiate and adopt policies, the UK has been in the minority (voting "No") on 57 legislative acts while supporting 2,474 acts.
There are many concerns about the economy
Before the referendum, the Treasury estimated that a Leave vote would lead to a reduction in the value of sterling of between 12 and 15 per cent.
Since the referendum on June 23, the value of the pound has dropped - from around 1.3 euros in June 2016 to around 1.15 euros now.
It was expected to be an expected short-term consequence of a Leave vote, but NIESR believes it would have a permanent impact, impacting the cost of imported products, as well as things such as holidays.
But the EU is struggling itself. Despite years of attempted austerity and economic reforms, the European Union is still facing an economic crisis, with unemployment and debt at eye-watering levels in some predominantly Mediterranean countries.
Greece's debt stood at 177.4 per cent of GDP in 2015 - and it's not the only EU country to be drowning in debt.
Some of these economic concerns are based around the single market
As part of the EU, the UK has access to free trade among a single market of 500m people - leading to concerns that the UK's confirmed departure of this could lead to an economic slowdown.
In 2016, the UK exported £142.7bn worth of products and services to the EU, while it imported £236.7bn in return. This led to a trade deficit of £94bn in 2016 - up from £42.8 in 2010.
After the UK has left, the Government will hope to make free trade deals with countries outside of Europe.
While the EU is the UK's largest trade market, the United States and China are also some of the most significant partners for British trade, and will be areas with which Theresa May will hope to boost connections.
Preserving the union is a priority
Scotland and Northern Ireland both voted to remain in the European Union - and Theresa May has said that preserving the union will be a priority within her negotiations.
Scotland's constitutional relationship with the United Kingdom and the European Union is complex. Nicola Sturgeon has announced her plans for a second Scottish independence referendum, arguing that Scotland didn't vote for the risks she foresees from a hard Brexit.
Some 55 per cent of Scots voted against Scottish independence, while 62 per cent voted to Remain last year. Sturgeon's hope is that she can win over the pro-Union Remain voters while ensuring, at the same time, that SNP-supporting Brexit voters are not alienated.
The Prime Minister will have to keep this balance is mind if she is to keep a post-Brexit Britain together.
Theresa May’s plan has the public's backing - even among Remainers
Theresa May's personal approval ratings are high - much higher than her party's. And this has extended to her plans for Brexit.
When asked if they think that May's plans respect the result of the referendum, 62 per cent of people replied positively - including 56 per cent of Remainers.
They do so grudgingly, with only 28 per cent of them being personally happy with the outcome. But they still accept that May's approach is respecting the referendum result that saw 52 per cent vote for Brexit.
When it comes to the European Union's reaction to the British approach, just one in five think that it will agree to the deal.
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