Image source, PA Media

On day one, Lady Hale, the most senior judge in the UK, said the case surrounding Boris Johnson's suspension of Parliament raises "a serious and difficult question of law".

In her opening statement, she said: "That this is a serious and difficult question of law is amply demonstrated by the fact that three senior judges in Scotland have reached a different conclusion from three senior judges in England and Wales."

She said the court would endeavour to address these questions, but would not determine "wider political questions" relating to the Brexit process or have any impact on its timing.

Read more from day one of the Supreme Court hearing.

BBC legal correspondent Clive Coleman takes a look inside the courtroom where the case will be heard.

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New justices are appointed by the Queen on the recommendation of a panel of legal experts from each of the UK's nations.

Applicants must have been a High Court judge for at least two years or a practising lawyer for 15.

Dominic Casciani
Home Affairs Correspondent

Image source, UK Supreme Court

The question for the Supreme Court is twofold.

First, do judges have the power to intervene in how a PM prorogues Parliament?

And, if they do, was Edinburgh's court right to conclude Mr Johnson had acted unlawfully in closing it for such a long period?

On a simple level, the justices have to decide whether or not the PM acted lawfully. If Mr Johnson loses, the question then would be what kind of action the court orders.

If the judges rule prorogation was legal, Parliament will remain shut until 14 October - unless the government advises the Queen to recall MPs at an earlier date.

Ms Miller's lawyers are, however, asking the justices for a repeat of the declaration from Edinburgh's Court of Session that the PM's actions were "null and void and of no legal effect".

If her side wins, it's still unclear how and when Parliament would resume.

Wednesday: It's time for the respondents - those who are defending the appeals, and want them to be upheld - to have their chance to reply.

First up will be PM Boris Johnson's lawyer, Sir James Eadie. He will respond to the appeal from Gina Miller, who wants to overturn the High Court ruling which found the suspension of Parliament was lawful.

Then, in the afternoon, it's Aidan O'Neill, the lawyer for the group led by SNP MP Joanna Cherry. They want the Scottish court ruling, which found the suspension of Parliament was unlawful, to be upheld. The UK government are trying to overturn the Scottish ruling.

Thursday:There are submissions from those who have been given permission to intervene in the appeals.

Among those making submissions are former PM Sir John Major.

When's the ruling announced? The timing of when the court may rule remains unclear.

Dominic Casciani
Home Affairs Correspondent

It is the highest court in the United Kingdom. The judges, known as justices, have the final say on the biggest legal issues and are the ultimate check and balance on the UK's laws and constitution.

The justices only hear the cases that raise what they consider to be a genuinely important point about how the UK's laws should be interpreted and applied - that is about one in three cases referred to it.

The court sits opposite the Houses of Parliament, its location symbolising the relationship between the two: Parliament makes the laws and the Supreme Court oversees their fair and just use.

BBC Radio 5 Live

Public law expert Dr Stefan Theil, from Oxford University, says after watching yesterday's proceedings: "You can can really tell that the judges are taking their time, they're really carefully considering what's going on.

"It's very difficult to read what they're thinking," he adds.

"At the moment you think you can draw an inference from one question, the justice turns it around and asks a question that goes in a different direction".

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Gina Miller has been at the forefront of two key legal battles over Brexit - the fight to get MPs to vote on whether the UK can start the process of leaving the EU, and the challenge to the government's decision to suspend Parliament before the Brexit deadline.

But who is she?

You can read our profile of Ms Miller here.

On Tuesday, QC Lord Pannick told the Supreme Court that Boris Johnson suspended Parliament to avoid the risk of MPs "frustrating or damaging" the PM's Brexit plans.

He also said there was "strong evidence" that Mr Johnson saw MPs as "an obstacle" and wanted to "silence" them.

On Tuesday, the Advocate General for Scotland, Lord Keen QC, told the Supreme Court that the prime minister is "entitled" to suspend Parliament for legitimate political reasons.

Speaking on behalf of the government, Lord Keen said it's not for the courts to decide what is a "legitimate political reason" and what isn't.

Today Programme
BBC Radio 4

Was prorogation a matter for the courts or a purely political decision that judges should not get involved in?

Stephen Tierney of the Edinburgh Law School tells the programme: “It is for Parliament alone to demarcate its sovereign relationship with the crown."

The professor explains that the crown - in this case represented by the prime minister, or executive - is controlled by Parliament.

"Our constitution prescribes appropriate jurisdictional limits," he adds. "If the court feels it can review prorogation, why would it not review legal statutes as well?"

Image source, UK Supreme Court

Cross-party peer Lord Pannick QC spent yesterday morning arguing on behalf of Ms Miller in her appeal against the English court's ruling.

He said Mr Johnson had suspended Parliament to avoid the risk of MPs "frustrating or damaging" his Brexit plans.

Lord Pannick said he had no quarrel with a prime minister's right to prorogue Parliament in order to present a Queen's Speech.

But he said the "exceptional length" of this suspension was "strong evidence the prime minister's motive was to silence Parliament because he sees Parliament as an obstacle".

The afternoon saw the Advocate General for Scotland, Lord Keen QC, arguing on behalf of the government against the ruling from the Scottish courts, which said prorogation was "unlawful".

He said previous prorogations of Parliament - including in 1930 and 1948 - had "clearly been employed" when governments wanted to "pursue a particular political objective", adding: "They are entitled to do so."

And he added that if MPs did not want Parliament to be suspended, they had "adequate mechanisms" and opportunities to stop it in its tracks by passing new laws - pointing to the fact a bill to block a no-deal Brexit was passed in just two days.

Businesswoman Gina Miller's team is appealing against the English High Court decision that prorogation was "purely political" and therefore "not a matter" for the judiciary.

And the government is appealing a ruling by judges at Edinburgh's Court of Session, who said the move by Mr Johnson was "unlawful" and aimed to "stymie" MPs ahead of the Brexit deadline.

Good morning and welcome to day two of our coverage of the Supreme Court, which is hearing challenges to the PM’s suspension of Parliament.

The 11 judges are hearing two different appeals over the prorogation – one from the English High Court and one from the Scottish Court of session.

On day one of the hearing, government lawyer Lord Keen QC said the PM was "entitled" to act as he did and the issue was not one for the courts.

But Lord Pannick QC, acting for campaigners, against the move told the Supreme Court it was done to "silence" MPs ahead of Brexit.

Today’s session gets under way at 10:30 BST.