We are already getting into quite detailed legal and constitutional arguments, only briefly interrupted by someone sneezing in the courtroom.

Attorney General Jeremy Wright, for the government, says that Parliament has had multiple opportunities when passing legislation on the EU and other constitutional matters to circumscribe the government's executive powers, but it did so "only sparingly and explicitly".

To make his point, he runs through all the legislation passed in recent years on the EU, focusing on the 2015 Referendum Act - adding that Parliament is "sovereign" to impose whatever controls it wants on prerogative powers.

Parliament has the right to stand up for itself, he insists, and that despite having the "full capacity and multiple opportunities" to limit the executive's powers in this regard, it had decided not to do so.

In language that you might expect to hear in Parliament rather than a courtroom, Mr Wright said the prerogative power did not emerge "on a whim or come out of a blue sky" but had been "deliberately and definitively" granted to governments by successive Parliaments over the years. 

As is inevitable these days, there's no escaping the glare of social media for those appearing in the background of proceedings...

Jeremy Wright, who along with being the Attorney General is a Conservative MP, starts developing his arguments by giving a brief precis of how the UK came to hold a referendum on EU membership and what the result was - pointing out that there was a "clear" decision to leave the EU.

He refers to the High Court ruling about the need for the government to consult Parliament - arguing that while he respected the decision it was the government's opinion that it was mistaken.

He rejects suggestions that the government was undermining Parliament by not seeking their authorisation before beginning official Brexit talks - saying the use of executive powers is "in line with parliamentary sovereignty and public expectation" about how the referendum result would be implemented.

Such executive powers are widely used in treaty making, he asserts, saying it is not an "ancient relic but a constitutional necessity". 

Image source, AP

Remember #dogsatpollingstations from the general election and referendum? It seems they may be making a comeback for the Article 50 court case...

Lord Neuberger concludes his brief opening address and gives the floor to Attorney General Jeremy Wright, who is leading the government's legal team.

He starts by saying that the issues at stake are of "great constitutional significance" and that there is "understandable and legitimate" interest in the case both inside and outside the courtroom.

He goes on to defend the right of the court to decide the matter - that's a clear endorsement of the judiciary and a rebuff to those who argue that it has no place intervening - saying it is "perfectly proper" for it to do so.

Lord Neuberger moves on to the background to the court case. 

The court’s task, he says, is to “decide points of law which fall within its jurisdiction”. While there is major public interest in the case and he is aware of the strong feelings associated about the Brexit vote and its political consequences, he says the court must disregard those.

Lord Neuberger goes on to say that no-one involved in the case has asked any of the 11 justices to stand down and he thanks the legal teams for ensuring the hearing can be conducted in an “orderly fashion”.

He remarks on the fact that there are more than 100 members of the public in the court and adjacent rooms, saying how “keen” the court was to accommodate them. The proceedings are being broadcast live on its website and TV and this is a key embodiment of “open justice”.

He tells the lawyers that the large number of written submissions means that there will be less time for oral arguments and gently reminds all the advocates to keep to their brief.

BBC Radio 2 presenter Jeremy Vine held a poll on Twitter today. Is this the answer you expected?

Various individuals have, Lord Neuberger says, received “threats of serious violence and unpleasant abuse” on social media simply for exercising their “fundamental right” to go to court.

This is believed to be primarily a reference to Gina Miller, the woman who brought the case against the government, who has said she has received death threats.

This abuse, he argues, “undermines the rule of law” and the court has the power to ensure its proceedings remain “available to everyone”.

Lord Neuberger, the president of the Supreme Court, is now making some opening remarks.

He starts by warning the media and anyone else not to publish certain personal details about those involved in the case including their home addresses.  He says he is particularly concerned about protecting participants who have children.

The scene is set in the courtroom as the 10 men and one woman hearing the case enter, and the proceedings begin. 

We are minutes away from the start of the hearing, which could become the most watched legal event in British history. (although it is worth saying that not that many events have been televised in the past...)

Victoria Derbyshire

Martin Howe QC, chairman of Lawyers for Britain, is supporting the government's case at the Supreme court. 

"The challengers in this case are relying on their rights, but what we have to remember is other people have rights too," he told the Victoria Derbyshire programme. "There were over 17 million who voted to leave the European Union and their rights should be respected.

"Parliament itself decided that it should be a decision taken by the British people. There is no need for yet another act of parliament simply to carry out the decision of the British people."

But Alison Young, professor of public law at Oxford University, said it was a case about something different. 

"Although there was a decision by the British people about leaving the European Union, this case isn't about whether we should leave, this case is asking legally how do we do this in the correct manner."

Sky News

Labour MP Gisela Stuart says the question before the court about the respective powers of the executive and Parliament is relatively "straight forward" and should not be confused with the wider question of what kind of Brexit there will be. 

The MP, who was chair of the Vote Leave campaign, says the political complication is about the timing of triggering Article 50 - that's the formal mechanism for beginning exit talks - not whether it happens. 

It is "quite important" that Prime Minister Theresa May is allowed to proceed on schedule and begin official Brexit talks by the end of March, she adds. 

Sky News

Conservative MP Anna Soubry, a keen Remain supporter, says there has been a lot of "misinformation" about the case.

She tells Sky News it is not about thwarting Brexit but upholding the constitution and the integrity of the judiciary. The judges, she believes, will make a judgement "free of emotion, free of politics and do the right thing by our constitution".

The former minister says she "strongly advises" the government to get on with putting legislation before the Commons to enable it to activate Article 50, believing that it will get the overwhelming support of MPs. 

Although a strong believer in EU membership, she says she will vote for Article 50 and only knows a handful of MPs who will vote against. 

Victoria Derbyshire

Ian and Nigel Baxter are brothers and businessmen based in Nottingham. But the referendum came between the pair and they are still arguing about whether this case is worthwhile. 

"I am very frustrated by it," Nigel told the Victoria Derbyshire programme. "Whilst the merits may be constitutionally right, all this is is a frustrating tactic from the European Union and creating problems for our Prime Minister which are completely unnecessary."

But Ian could not feel more differently to his sibling. 

"We live in a parliamentary democracy don't we?," he said. "I voted to remain, I accept the result, but the triggering of Article 50 is something parliament should agree to and arrange. The government should come to parliament and explain the strategy they have for leaving the European Union."

Image source, Reuters

On 23 June, the UK public voted to leave the European Union by a margin of 51.9% to 48.1%. More than 33 million people voted in the referendum.

Whatever the court decides, it will not invalidate the referendum result or halt the Brexit process.

Should the government lose the case, it is expected to ask MPs and peers to give it permission to activate Article 50, either through legislation or a motion - which could be fast-tracked through Parliament.  

Given that nearly all Conservatives and many Labour MPs have said they will vote for this, it should pass easily. The situation in the Lords - where there are hundreds of crossbenchers - is less predictable but it would still be a major shock and something of a constitutional crisis if they voted against it.

This week's case is also unlikely to have a major impact on the terms of UK exit. That will be decided in detailed negotiations over the next few years.

But what is at stake is who has the right to initiate the Brexit process - the government or Parliament - and in more general terms a question of where the will of the people, as expressed by the referendum result, resides. In this respect, the decision of the Supreme Court could have a major impact on wider relations between the executive and legislature in future and their respective powers.

Writing in the Financial Times, external, David Allen Green reminds us what today's court case is not about today. 

"This appeal is not about blocking Brexit," he wrote. "The case is instead about the constitutionally correct manner in which the notification to leave the EU should be given. 

"The case is ultimately about constitutional form and process, rather than the substance and merits of the Brexit decision."  

It is a very British way of fighting it out, according to this Daily Telegraph reporter.