Legal correspondent, BBC News
Legal correspondent, BBC News
The Supreme Court has been preparing for this unprecedented case, from where the judges will be sat through to how many cups of tea they expect to drink over the next four days.
Here is the Article 50 case in numbers...
Scotland and Wales are being represented in the court case this week, ensuring both devolved governments get the chance to make their cases to the Supreme Court.
Stephen Gethins MP, of the Scottish National Party, told the Victoria Derbyshire programme: "We live in a parliamentary democracy and since vote leave didn't give us any details about what their plans were, it is right that we scrutinise any plans.
"Furthermore, democracy doesn't begin and end in Westminster. Any plans to leave the European Union will have a significant impact on the areas of responsibilities of the Scottish Parliament, as well as the Welsh Assembly and in Northern Ireland as well so it is only right and proper that the Scottish parliament has a say."
Leanne Wood, leader of Plaid Cymru, said: "We accept people in Wales decided to leave. It's the how now. The incompetence and rudderlessness that we see from the Tories in Westminster the lack of a plan, the incoherence..l. there are grave dangers for Wales."
But Anne Marie Trevelyan, the Conservative MP for Berwick upon Tweed, said: "The government is being very clear. There is a very clear mandate for leave."
Ahead of the start of the Supreme Court hearing, ministers have insisted they have a "strong case" and will "robustly defend" their position.
In recent weeks, the government has made clear that it will be relying on the same arguments as it did in the High Court case - namely that the power to make and withdraw from international treaties rests with the executive through the use of prerogative powers and that Parliament has had numerous opportunities to circumscribe those powers in recent years but decided not to.
A government spokesman said it would not be derailed from its broader political course - which is to begin the official exit process from the EU by the Spring.
Quote Message: We are determined to respect the will of the British people who voted to leave the EU and are committed to triggering Article 50 by the end of March next year. Our timetable has not changed."
The site of the Supreme Court is being described as "a media circus" with queues of people trying to get in, journalists trying to get a story and protesters trying to make their voices heard.
Here are some tweets from people at the scene.
The Daily Telegraph
Former Tory leader and Brexit supporter Lord Howard has written in The Daily Telegraph, saying he believes triggering Article 50 will stay on track, whatever the decision for the court.
He said: "Those of us who are committed to the implementation of the referendum need not despair, even if the decision of the Divisional Court is upheld.
"The Government, we are told, has prepared the legislation that will be needed if that is the way the Supreme Court rules. I do not believe the House of Commons will be prepared to affront the majority of the electorate by voting it down."
Gina Miller has arrived at the Supreme Court for Monday's hearing. Writing in the Guardian earlier, the finance manager said the hostile coverage she had received over her legal challenge meant she could no longer travel on public transport, work in her office, or even spend a normal weekend with her family. She suggested that some people had even incited violence against her.
Quote Message: I don’t go anywhere – it has been a complete poisoned chalice."
Ms Miller, who has previously said she has received death threats, insisted that her actions were borne out of her desire to uphold parliamentary sovereignty rather than thwart the referendum decision.
Quote Message: We would be undoing 400 years of democracy and sovereignty if the government were allowed to use this royal prerogative."
Here are some of the other stories around today apart from the Supreme Court case:
BBC Radio 4
The government is seeking to overturn last month's High Court ruling - in which a three-man bench led by the Lord Justice Lord Judge decided that only Parliament had the authority to trigger Article 50 and the prime minister must seek the consent of MPs and peers before doingso.
The ruling sparked controversy with a number of newspapers attacking Lord Judge and his colleagues and accusing them of trying to frustrate the will of the people and overturn the referendum vote. One front page described them as "enemies of the people".
Labour shadow attorney general, former Liberty director Shami Chakrabarti, told the BBC the criticism had "verged of vilification" and was intolerable.
Quote Message: The judges are not fair game. They cannot speak up for themselves and we all need them in the end if we are going to settle our disputes in a civilised way in the courtroom
Lawyers and supporters are arriving at the court alongside our legal correspondent Clive Coleman.
There are reports of a police presence, as well as supporters from both sides of the argument turning out for the case.
"I have never seen anything like this," he told the BBC News Channel. "The world's press, the public queuing up, demonstrators dressed as judges, the atmosphere is quite extraordinary."
Labour leader Jeremy Corbyn has said his party will seek to amend Article 50, before the court case to decide whether it needs to be brought in front of parliament has even taken place.
The Islington MP told Sky News he respected the result of June's referendum, but he wanted to ensure Britain maintained access to Europe's markets, workers' rights and environmental protection measures.
Who are the main characters in this courtroom drama?
The Brexit case, unsurprisingly, has attracted quite a lot of public and media interest. As well as the live broadcast on the BBC, the Supreme Court will have its own live feed of proceedings. It will be publishing twice-daily transcripts on its website of what is said at about 1600 BST and 1900 BST.
The court has created additional seating for about 115 members of the public to watch the action in the court itself and adjacent rooms. More than 80 journalists from around the world have been accredited to cover the event.
One final but rather significant point to note - we will have to wait a little for the final judgement. It won't be handed down on Thursday at the end of the play but will be reserved until a later date. That means we are not expected to know the outcome until next year, probably in January.
Given the legal and political magnitude of the issue at stake, we should not be surprised that the justices may want as much time as possible to deliberate and reach a definitive conclusion. But what happens if they don't?
The BBC's Clive Coleman says there is a "slim chance" that they may decide to refer the case to the European Court of Justice for clarification which, he adds, would be a "bitter irony" given the case resolves around the supremacy of Parliament and the laws that it passes.
What's the Supreme Court case all about and what could it mean for Theresa May's Brexit strategy? The BBC's legal correspondent Clive Coleman has been examining the main points of law that will be contested and the two sides' likely arguments over issues such as prerogative powers and parliamentary sovereignty. Read his analysis here. What about the politics? Remember prime minister Theresa May has said she intends to officially notify the EU of the UK's decision to leave - thereby triggering formal talks on the process of separation - by the end of March. Should the government lose the case, and that is a big if, that could set the cat among the pigeons and potentially endanger her timetable. The BBC's parliamentary correspondent Mark D'Arcy has been looking at what could happen in this scenario and the government's possible options as it seeks to press ahead with implementing June's referendum vote.
Good morning and welcome. It is not often that the eyes of ministers, MPs and commentators are fixed on the Supreme Court but that will be the case for the next four days. The 11 justices in the highest court in the land will sit on a potentially landmark case with major ramifications for the UK's exit from the EU. The judges will hear the government's appeal against last month's High Court ruling which stated that Parliament's consent was needed before the official Article 50 Brexit process could begin. Monday's proceedings, to be live streamed by the BBC, will begin at 11:00 GMT.