Peter Nicholls | WPA Pool | Getty Images

The U.K. and the European Union are finally about to start discussing the nitty-gritty of how the former will leave the bloc - an unprecedented moment in European history. British and European officials are gathering in Brussels Monday. On the table will be decisions such as how much the U.K. needs to pay the EU before it leaves. CNBC takes a look at the key players in the negotiations who will determine how the U.K. is going to leave the Union, and what its future relationship with the trading bloc will be.

Theresa May, UK prime minister

British Prime Minister Theresa May delivers her keynote speech on Brexit at Lancaster House on January 17, 2017 in London, England. Getty Images

Understandably, May wants to make a "success out of Brexit." The prime minister has stated she is keen on leaving the EU so that the U.K. can regain control of the number of migrants from Europe and beyond. But there are concerns that after losing a parliamentary majority her negotiating position will be weakened and she will forced to take a softer approach.

David Davis, UK secretary of state for Exiting the European Union

Jack Taylor | Getty Images

His task is to negotiate with the EU on behalf of the U.K. government. This includes listening to Scotland, Wales and the Northern Ireland. He has admitted that the U.K. is preparing contingency plans in case it doesn't reach an agreement with the EU within the two-year time limit set on the talks.

Phillip Hammond, UK Finance minister

New Chancellor Philip Hammond arrives at Downing Street on July 13, 2016 in London, England. Carl Court/Getty Images

Though the U.K.'s Finance minister will not be at the negotiating table, Hammond will be key to advise on the financial impact that certain negotiating points will have on the British economy. Perhaps the biggest issue is the future of the City of London.

Liam Fox, UK secretary of state for International Trade

Simon Dawson | Bloomberg | Getty Images

The U.K. doesn't want to retain access to the single market. Instead, it wants to work on a new trade deal with the EU - at least this was the negotiating stance before the General Election early June. Designing a trade agreement normally take more than the two-year limit for the Brexit talks. Fox is also responsible for preparing the ground for trade deals with other countries in the world and attempt to offset the economic impact of leaving the EU's single market.

Boris Johnson, UK Foreign secretary

Former London Mayor and 'Vote Leave' campaigner Boris Johnson speaks during a press conference in central London on June 24, 2016. Mary Turner | AFP | Getty Images

The former mayor of London is one of the most notorious Brexit supporters. Johnson said that it would be "perfectly okay" if the U.K. was unable to reach a deal with the EU within the two-year deadline. Many economists and international bodies say otherwise.

Michel Barnier, Europe’s chief negotiator

Michel Barnier during a news conference after a meeting of EU finance ministers at the European Council headquarters in Brussels, Belgium. Jasper Juinen | Bloomberg | Getty Images

He's the leading negotiator on behalf of the other 27 EU countries. Apart from having to include the demands from all member states, the French politician also has to listen to European lawmakers and defend their interests in talks with the U.K.

Guy Verhofstadt, Brexit chief for the European Parliament

Guy Verhofstadt, the European Union's lead Brexit negotiator. Thomas Samson | AFP | Getty Images

The Belgian politician is responsible for representing the views of all the lawmakers sitting in the European Parliament. In the eventuality that the U.K. and the EU agree to set up a new trade deal, the European Parliament will have to approve it.

Donald Tusk, president of the European Council

Donald Tusk Simona Granati | Corbis | Getty Images

The president of the European Council represents all heads of state. He is also the chair of all European summits. Tusk said recently that EU27 unity is the most important condition for a positive outcome.

Jean-Claude Juncker, president of the European Commission

Jean-Claude Juncker speaks during a media conference at EU headquarters in Brussels. Dursun Aydemir | Anadolu Agency | Getty Images

Juncker won't be sitting at the negotiating table but he will want to follow this issue very closely. He's the head of the Commission, responsible for proposing legislation, and the first country leaving the EU will happen during his time in office. However, he has said he believes the U.K. will re-join the EU.

Angela Merkel, chancellor of Germany

Angela Merkel Thierry Charlier | AFP | Getty Images

The powerful German leader – seen as a crucial figure leading the EU - is not going to be in the negotiations with the U.K. but her voice will certainly be important. Merkel has said that the Brexit vote should be a wakeup call to the EU and the remaining countries should press ahead with integration though at different speeds.

Emmanuel Macron, president of France

Emmanuel Macron addresses supporters after winning the French Presidential Election, at The Louvre on May 7, 2017 in Paris, France. David Ramos | Getty Images