If they conclude Begum has no right to return to be at her appeal in person, the five justices may also decide she has no right to appeal in the first place—effectively ending her attempts to have her citizenship returned.
The hearing will last for two days.
Begum travelled to Syria at the age of 15, along with some other classmates, to join the so-called ISIS caliphate.
As the caliphate was being whittled down to its last survivors by U.S. and allied forces, she surfaced at a refugee camp in Syria, where she caught the interest of Western journalists.
Her citizenship was revoked in February last year by the Home Secretary following a series of interviews she gave from the refugee camp in which she expressed little remorse but said she wanted to return to the UK.
Her family launched a legal appeal against the decision. Their legal team also say that Begum must be allowed to return to the UK so that she can give evidence in person. The government has resisted in the courts.
Begum has dual British-Bangladeshi citizenship.
The Home Secretary at the time, Sajid Javid, said that Begum represented a security risk.
The government has taken the case to the Supreme Court.
"Ms Begum sought leave to enter the UK so that she could pursue an appeal against this decision, but her application for leave to enter was refused. Ms Begum challenges both the decision to deprive her of citizenship and the decision to refuse her leave to enter the UK."
The Supreme Court says the hearing will answer three questions:
First, should she be granted leave to enter the UK to pursue her appeal against having her British citizenship revoked?
Second, if the court decides she has no right to return to make her case, should her appeal against the deprivation decision be allowed at all?
Third, was the Special Immigration Appeals Commission (SIAC) wrong to apply judicial review principles to her appeal against the deprivation decision?
That last question relates to the conclusion by SIAC that because Begum is currently detained by the Syrian Democratic Forces in a camp, she can't give effective legal instructions or take any meaningful part in her appeal.
It was on these grounds that the Court of Appeal in July said Begum should be allowed to return to pursue her appeal in person.
The government says that the judicial review principles used by SIAC should not apply to someone whose citizenship has been revoked.