As everyone who hasn't been living under a rock knows, yesterday Dobbs v. Jackson Women's Health Organization was formally decided. The decision was over the constitutional status of Missouri's Gestational Age Act (2018), which restricted abortion to (1) gestation prior to 15 weeks, (2) medical emergency, and (3) fetal abnormality. The state was sued by a clinic that had been doing abortions up to 16 weeks. The Supreme Court ruled 6-3 that the law was constitutional and 5-4 to overturn Roe v. Wade and Planned Parenthood v. Casey, thus returning the matter to the states. It is not, I think, an accident that the basic structure of the majority opinion argument follows that of a recent majority opinion written by Ruth Bader Ginsberg, Timbs v. Indiana (2019).
What will happen next, we don't know. One reason Roe lasted fifty years despite the obvious problems with it and the need to keep tweaking it with other court cases, like Casey, was that its basic idea was an equilibrium-point between the pro-choice and pro-life movements as they then existed, and because of that it seemed almost immutable for a long time. What the new equilibrium will be, is yet to be determined. We're going to have a period of scrambling, for a few reasons:
(1) Some anti-abortion laws were never taken off the books. Abortion was a crime in all fifty states when Roe was handed down, and had been for almost a hundred years. After Roe, some states removed the laws from their codes, and some never bothered to do so. This is, I think, a good example of how thinking that a court "strikes down" laws is potentially very harmful. Courts are not legislatures, and they do not have after-the-fact veto power. When a court declares a law unconstitutional, it doesn't erase the law, it merely impedes its effect -- it can't be implemented. But if the law is not removed by the legislature and the decision declaring that it was unconstitutional is reversed, the law comes back into effect. There are states (Michigan seems to be one, for instance) in which politicians will be rushing actually to repeal or replace laws that they had been treating as no longer existing.
(2) Some states passed 'trigger laws' in case Roe was overturned. All of these are suddenly coming into effect, and states will have to adjust in order to implement them.
(3) Some states will polarize in inconsistent ways. As far as public opinion goes, states are all over the place. What will happen is that some states with restrictive laws will make their laws stricter, now that Roe no longer blocks them, while some states with permissive laws will make their laws more permissive to compensate for stricter states and to signal that they are in favor of a right to abortion. In some cases, this will bounce around quite a bit in the usual dynamic of controversial questions at the state level, as state legislators discover what their constituencies are willing to accept.
In the long run, however, I suspect it will have less of an effect than most people expect; Roe was not the only factor in the controversies, by any means. Abortion rights organizations will develop workarounds -- in fact, are working on doing so right now -- and will almost certainly be very well funded in doing so. Given the geographical distribution of the current laws, and the fact that crossing state borders is fairly easy today, my guess is that maybe ten percent of abortions will be seriously impeded by restrictive laws, and most will in fact be unaffected at all. A lot depends on how long the current make-up of the Supreme Court stays in place. New laws will sprout up in unpredictable ways, and state courts may well find ways to cram a right to abortion into some provision or other of state constitutions. (In some states, like Florida, abortion rights are already a part of the state constitution as it has been interpreted by the courts.) But in any case, it's possible that we are in for a quarter-century at least of a non-Roe regime.