The landmark hearing will determine whether British Prime Minister Theresa May must get Parliament to ratify her decision to invoke Article 50, which will trigger the official negotiations for Britain's exit from the European Union (EU).
The Supreme Court, which sits in central London, is made up of 11 justices who will hear the government appeal against last month's High Court ruling. The hearing is expected to last four days, with the verdict due early next year.
May has said she intends to officially notify the rest of the 27-member economic bloc of the UK's intention to leave - beginning two years of talks over the terms of separation - by the end of March 2017.
However, that timeline could be affected based on the Supreme Court ruling this week.
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The government's legal team had argued in the High Court that the public referendum in favour ofBrexitin June and ministerial powers mean MPs do not need to vote, but campaigners had argued this was unconstitutional.
The challenge had been brought by a group of businesses led by investment manager Gina Miller, whose lawyersargued that the government cannot trigger Article 50 of the Lisbon Treaty unilaterally despite a public referendum in favour of leaving the European Union (EU).
"The result today is about all of us. It's not about me or my team. It's about our United Kingdom and all our futures," Miller said after the judgement.
Ministers argued they can act under ancient powers of Royal Prerogative, the preserve of monarchies.
A judicial review of the issue in the HighCourtwas heard by the Lord Chief Justice of England and Wales, Lord Thomas, who announced their ruling today.
"The government does not have power under the Crown's prerogative to give notice pursuant to Article 50 for the UK to withdraw from the European Union," he declared.
The losing side in the case was always expected to launch an appeal, which was fast-tracked to the SupremeCourt.
The EU's other 27 members have said negotiations about the terms of the UK'sexit- due to last two years - cannot begin until Article 50 has been invoked.