The Court, still missing a replacement for conservative justice Antonin Scalia, voted 5-3 that the Texas restrictions were unconstitutional. You can read the majority opinion, along with two dissenting opinions, below:
Rights v. Restrictions
Roe v. Wade guaranteed a woman's constitutional right to an abortion, but also recognized that the "State has a legitimate interest in seeing to it that abortion, like any other medical procedure, is performed under circumstances that insure maximum safety for the patient." Therefore, states are permitted to pass certain laws to protect abortion patients. That said, those restrictions can't place an undue burden on the right to an abortion, even if they allegedly have the woman's best interest in mind.
In another abortion case, Planned Parenthood v. Casey, the Court said, "[u]nnecessary health regulations that have the purpose or effect of presenting a substantial obstacle to a woman seeking an abortion impose an undue burden on the right," and even "a statute which, while furthering [a] valid state interest, has the effect of placing a substantial obstacle in the path of a woman's choice cannot be considered a permissible means of serving its legitimate ends."
So the question in this case wasn't whether Texas was allowed to pass any laws regulating abortions in the state, but whether two particular restrictions placed an undue burden on the right to receive an abortion.
When Are You Undue?
The Texas statute at issue required abortion clinic facilities to adhere to hospital-grade regulations, from corridor width, elevator size, and the swinging motion of doors to floor tiles, parking spaces, and even the angle that water flows from drinking fountains. Many Texas clinics failed to meet these standards and lacked the funds to upgrade.
The law also required abortion doctors to have "admitting privileges," at a hospital within 30 miles of the clinic in order to treat patients needing surgery or other critical care. This kind of formal affiliation can be hard to obtain, and many abortion providers found it impossible. The combination of the two laws meant that 20 of the Texas's 41 abortion facilities were forced to close already, an estimated ten to twelve more would need to shut their doors, and many women would be more than 200 miles from the nearest abortion provider.
The Supreme Court decided these restrictions placed an undue burden on a woman's right to an abortion. In writing the majority opinion, Justice Breyer held, "that neither of these provisions offers medical benefits sufficient to justify the burdens upon access that each imposes. Each places a substantial obstacle in the path of women seeking a pre-viability abortion, each constitutes an undue burden on abortion access, and each violates the federal Constitution."
The Court's ruling is expected to reverberate beyond the borders of the Lone Star State - 10 other states have admitting privileges restrictions and 23 require abortion clinics to become certified as ambulatory surgical centers. You can see the Supreme Court's full reasoning below: