Both sides of the debate regard this case as an all-or-nothing fight over abortion rights.
The first, 1973's Roe v Wade, gave women in the US an absolute right to an abortion in the first three months of pregnancy, and limited rights in the second trimester.
Nearly two decades later, in Planned Parenthood v Casey, the court ruled that states could not place an "undue burden" on women seeking abortions before foetal viability, about 24 weeks.
In the years since, foetal viability standard has acted as a key line in abortion law, preventing any bans an abortion before this time.
Representing Jackson Women's Health Organization - the only abortion clinic in Mississippi - Julie Rikelman of the Center for Reproductive Rights spoke next, asking the court to strike down the Mississippi law and maintain a woman's right to abortion.
If the court strikes down Roe v Wade, or rules that the Mississippi law does not place an undue burden on women seeking abortions before foetal viability, at least 21 states are expected to bring in more restrictive abortion laws.
Why abortion rights in US could be about to change?
Why abortion rights in US could be about to change