The three-day hearing includes appeals on three separate legal challenges to Prime Minister Boris Johnson’s plan to suspend parliament for five weeks.
Here’s a look at who launched the cases:
The English case: Gina Miller
High-profile anti-Brexit campaigner, Gina Miller, is appealing an English High Court decision to not issue an order lifting the suspension of Parliament. Judges said the suspension of Parliament is essentially a political decision for the Prime Minister.
But Miller says that suspending Parliament sets a horrifying precedent, and that Johnson’s government is “subverting democracy” in a way that is unprecedented.
John Major has joined Miller’s legal action, which means Britain is being treated to the extraordinary spectacle of a former Conservative prime minister suing his successor.
The Scottish case: Dozens of cross-party MPs
A cross-party group of more than 70 lawmakers, led by Scottish National Party MP Joanna Cherry, joined forces to sue the Prime Minister and prevent the suspension of Parliament.
Last week their case was successful, with Scotland’s highest court ruling that Johnson’s decision to suspend Parliament was motivated by the “improper purpose of stymying Parliament.”
The Supreme Court must now rule which set of judges — those in England or Scotland — was right.
The Northern Irish case: Raymond McCord
The Northern Irish appeal refers to Raymond McCord, a campaigner whose son was murdered by a pro-Unionist paramilitary group in 1997, aged 22.
Earlier this month, a Northern Irish court rejected his claim that the UK’s plan for a no-deal Brexit would break the terms of the Good Friday Agreement.
A no-deal Brexit would almost certainly lead to a need for some kind of infrastructure on or near the border between the Republic of Ireland, an EU member state, and Northern Ireland, which like the rest of the UK is leaving the bloc.
Boris Johnson’s suspension of Parliament in UK Supreme Court: Live updates – CNN International