On Wednesday it will consider a Mississippi law which asks the court to ban abortions after 15 weeks of pregnancy.
Its final ruling, due in June next year, could cut off abortion services for tens of millions of women.
What is the right to abortion in the US?
A woman’s right to abortion was established in 1973, following a Supreme Court ruling in a case known as Roe v Wade.
The decision gave women in the US an absolute right to an abortion in the first three months of pregnancy, and limited rights in the second three months.
Nearly two decades later the court made another key decision.
n Planned Parenthood v Casey, the court ruled that states could not place an “undue burden” on women seeking abortions before foetal viability.
In the US, this threshold for when foetuses can sustain life outside the womb has been set at about 23 or 24 weeks.
Why could a Mississippi law overturn Roe v Wade?
A state law was passed in Mississippi in 2018 which would make most abortions illegal after the first 15 weeks of pregnancy – including those caused by rape or incest.
It hasn’t been enforced due to a legal challenge by Mississippi’s only abortion provider, the Jackson Women’s Health Organization.
The US Supreme Court is now due to consider the case.
Mississippi is asking for Roe v Wade to be overturned, and with it the constitutional right to an abortion in the US.
If successful, states would be welcome to set their own standards for abortion – including outright bans before foetal viability.
Nearly two dozen states are expected to introduce their own bans, some probably more severe than Mississippi’s. BBC