The nature of Brexit will ultimately be decided by the governments of the 27 remaining EU nations and the UK. But the figures who negotiate the detail of the deal will be hugely important.
Many would argue that Germany's Angela Merkel and the UK's Theresa May are the two most important people in the Brexit negotiations.
But here are eight figures who will also be crucial to what happens.
Of the four from the UK, three are within the Exiting the EU department. On the EU side, the figures represent the Commission (the EU's executive cabinet), the Council (the leaders of each member state) and the parliament of elected MEPs, who will have to approve the final deal.
The EU negotiators
A seasoned master of French and EU diplomacy, chief negotiator Michel Barnier will go head-to-head with UK Brexit Secretary David Davis.
They used to be sparring partners in the 1990s, when they were rival Europe ministers with contrasting visions of the EU.
Like Mr Davis, Mr Barnier does not owe his current status to his country's elite club of politicians. He did not attend the prestigious Ecole Nationale d'Administration, incubator of French political high-flyers.
He has already given a clear indication of the tough stance he will take in negotiations - from guaranteeing the rights of Polish students and Romanian nurses in the UK, and British pensioners living in Spain.
He is also adamant that the "sequencing" of the talks is key - the UK won't get to negotiate a trade deal until separation terms are agreed that preserve the integrity of the EU single market, and the UK settles its outstanding bills.
Michel Barnier made his mark in French politics by organising the 1992 Winter Olympic Games in the French Alps. And for a long time he was regarded as a provincial - some called him "the ski instructor".
He served as France's Europe minister and was briefly foreign minister.
He stems from the Gaullist tradition. It was Charles De Gaulle who famously said "Non" to the UK joining the Common Market.
Since 2010, Mr Barnier has been big in Brussels. As internal market commissioner he had oversight of the City of London at a sensitive time - in the wake of the 2008 financial crisis. That role caused jitters in UK business circles, as Mr Barnier pushed through financial reforms.
While some in the City disapproved of new EU regulations on bank capital reserves and bankers' bonuses, other officials found him more accommodating to City interests later on. And his opposite numbers in the Brexit talks will hope for the same pragmatism.
Sabine Weyand - one of "the Commission's best and brightest", according to its president, Jean-Claude Juncker - was picked as Mr Barnier's deputy chief negotiator in September.
She studied at Cambridge University in the 1980s, and knows well the country whose exit from the EU she will be helping to engineer.
But this German national is best known as a veteran at representing the Commission and its interests. And that makes her a formidable opposite number.
She has 23 years' experience in trade relations and more than a decade at the Commission itself.
One Brussels lobby group predicted Ms Weyand was unlikely to give much ground in trade talks on any UK hopes of a la carte access to the EU, particularly any weakening of the EU single market ideal of free movement.
Those who have seen Ms Weyand in action speak highly of her as being far from a faceless cog in the Brussels machinery.
Cecile Toubeau, whose group campaigns for sustainable transport inside Europe, came into contact with her at the time the VW emissions scandal blew up in 2015.
"She was very straightforward, she got to the point quickly, she understood the issues that we were bringing," says Ms Toubeau. "She was open to what we said but I felt she was able to say, 'That's politically not something we can consider'.
"She was no-nonsense and honest - she really knew her stuff. She didn't need to look to her assistants for guidance."
In its list of the most influential women in Brussels, the politico.eu website put Ms Weyand at number eight, calling her a "Commission problem-solver".
She served in the cabinet of French former EU trade chief Pascal Lamy from 1999 to 2004, and later helped steer the EU's climate policies.
She also monitored national governments' economic and financial performance in the Commission's Secretariat-General.
In the run-up to the Brexit vote, Donald Tusk did all he could to find a deal to keep the UK in the EU. He was apocalyptic when he warned that the UK leaving could end "in the destruction of not only the EU but also Western political civilisation in its entirety".
His efforts came to nothing and as the result emerged he tried to calm the waters in Brussels, saying "what doesn't kill you, makes you stronger".
But in the wake of PM Theresa May's re-election without a parliamentary majority, he warned the UK to make up for lost negotiating time, tweeting: "We don't know when Brexit talks start. We know when they must end. Do your best to avoid a 'no deal' as result of 'no negotiations'."
As president of the European Council, his challenge is to keep Europe's leaders united as they negotiate Britain's exit.
Mr Tusk, a former Polish prime minister, is loathed by Poland's nationalist government that tried and failed to unseat him. But he has the respect of other European leaders for his handling of the conflict in eastern Ukraine, the migrant crisis and the Greek debt negotiations.
He has warned the UK not to expect to cherry-pick its way out of the EU and he has rejected British threats to walk away without a deal. But he has spoken of his aspiration for a "smooth divorce" with the two sides breaking up as "good friends".
Mr Tusk is from Poland's Kashubian minority and grew up in Gdansk, the Baltic port city where anti-communist demonstrations, led by the Solidarity trade union, erupted in the 1980s.
He was active in Solidarity while studying history at the University of Gdansk.
As prime minister, Mr Tusk led Civic Platform (PO), which espoused free market policies. His government cut jobs in the state sector, pursued privatisation, cut taxes to woo foreign investors and tried to persuade Poles abroad to come home.
Didier Seeuws, a hard-working diplomat with an eye for detail, was quickly tapped by Donald Tusk to head the Council's task force for the Brexit negotiations.
While the Barnier-Weyand Commission task force will do the "heavy lifting" in the negotiations - dealing with the technical detail of Britain's exit from the EU - the Council team will be tasked with keeping the remaining 27 national governments happy and shaping the EU's longer term strategic relationship with the UK.
Mr Seeuws will also have to bear in mind the views of MEPs - the European Parliament will have to approve the final deal.
Mr Seeuws's team is said to have been meeting twice a week in preparation for negotiations - prompting unhappy comparisons with the UK side's state of preparation in some of the media.
Mr Seeuws is respected for his role in handling the Greek debt negotiations - working through the night until dawn and overcoming divisions between heads of state to achieve a deal.
From 2007 to 2010, the 51-year-old technocrat from the Flemish city of Ghent was Belgium's deputy ambassador to the EU, where he is said to have negotiated a breakthrough on the European patent system - following a 30-year deadlock.
The ambassador he served under, Jean De Ruyt, told the BBC his political instincts were "always spot on" and that he "trusted his judgement and recommendations completely".
"Apparently modest and obliging, he is capable of mastering the most complex of technical issues and understanding immediately the political stakes, but at the same time able to explain in simple words what has been discussed or decided.
"I have no doubt that Didier will often be able to reach a fair compromise when, as expected, difficult negotiations will reach a stalemate."
Prior to this, Mr Seeuws served for several years as spokesman for the Belgian prime minister, none other than Guy Verhofstadt, the man chosen as chief Brexit negotiator for the European Parliament.
Eventually, Mr Seeuws took up a job as right-hand man to Donald Tusk's predecessor at the European Council, Herman van Rompuy. He has since worked at the Council as head of transport, telecommunication and energy.
The UK negotiators
Olly Robbins is the top UK official at the Brexit talks.
At the start of the process, he was the top civil servant in David Davis's Exiting the EU department.
But he has now moved to the Cabinet Office to work more directly for the prime minister, following reports of tensions with Mr Davis.
The move was seen as a sign of Theresa May taking more control of Brexit negotiations.
He cut his teeth at Gordon Brown's Treasury, helping to co-ordinate public spending policy, before going on to serve in senior behind-the-scenes roles for both Tony Blair and Mr Brown in Downing Street. By civil service standards, his rise was meteoric - he was Mr Blair's principal private secretary by the age of 31.
He gained a reputation for being a skilled mediator in the frequent disputes between No 10 and the Treasury.
"In all my dealings with him, he really embodied the essence of the impartial civil service, and he's very popular," former Olympics minister Lady Jowell, told website Politico.
After a spell as director of the civil service and as David Cameron's deputy national security adviser, Robbins became the senior civil servant in charge of immigration policy at Theresa May's home office.
When Mrs May became prime minister she drafted Robbins in as her senior EU adviser, prompting speculation the government wanted to put the free movement of people at the heart of Brexit negotiations.
Robbins generated some headlines in 2016 when he was ejected from a Home Affairs select Committee hearing by then chairman Keith Vaz for failing to give information about the UK Border Force's budget on time.
He was also caught on camera "grinning sheepishly" as Mrs May handed her handbag to him at an EU summit in Malta.
A career diplomat, with a reputation as a low-key but solid operator, Sir Tim Barrow was drafted into the role of UK ambassador to the EU following the resignation of Sir Ivan Rogers, who had accused the government of "muddled thinking" over Brexit.
Sir Tim was Britain's ambassador in Moscow between 2011 and 2015, a turbulent period in relations between the two nations, and previously served as Britain's ambassador to Ukraine.
The diplomat started his foreign office career in 1986 at the UK embassy in Brussels before going on to serve as a private secretary to Labour foreign secretary Robin Cook, advising on the EU, Russia and Middle East.
"It's the toughest negotiation in our lifetimes and I think he is up to it," Britain's former ambassador to Lebanon Tom Fletcher told BBC Radio 4's Today programme.
"I have seen him in Brussels. He knows the corridors, he knows the characters. But actually more importantly I saw him in Moscow where he was incredibly resilient as ambassador there, dealing with Putin in a very testing time in our relationship and Tim had a reputation of being bulletproof out there."
BBC diplomatic correspondent James Landale said Sir Tim was less likely to be criticised by Brexit supporters than some other potential candidates for the job, as it "would be very hard to say that Sir Tim Barrow is an out-and-out pro-European".
A fluent Russian speaker, Sir Tim was educated at Arnold Lodge in Leamington Spa, Warwickshire, and Oxford University.
As director general of the Department for Exiting the EU, Sarah Healey is, in effect, second-in-command of the civil service machine tasked with delivering Brexit.
She comes fresh from a similar role at the culture department and also led cross-government efforts to promote more women into senior civil service roles through job-sharing arrangements.
Her previous claim to fame was as a contestant on University Challenge - she won the BBC Two quiz in 1998 and twice competed in the Champions of Champions competition for Magdalen College, Oxford.
Healey studied modern history and English at Oxford and gained a postgraduate degree in social policy from the London School of Economics before embarking on a career in the civil service.
Her former boss at the culture department, Tory MP Ed Vaizey, told the Times she was "incredibly sharp and intelligent", adding "there are no flies on her at all".
She worked briefly for Iain Duncan Smith, when he was work and pensions secretary, and, before that, was director of strategy and funding at the education department under Michael Gove.
She recently told a think tank conference that, as a student of history, freedom of information was an issue "close to my heart".
"One of the things I reflected on when I took this job was that my children, if they were to take history degrees, would write essays on what we were doing so it was terribly important that they do have access to the archives of the time," she said.
Profiles by Becky Branford, Paul Kirby and Brian Wheeler. Illustrations by Gerry Fletcher.