The Supreme Court's decision in Dobbs v. Jackson Women's Health Organization overturned Roe v. Wade and concluded that the Fourteenth Amendment's Due Process clause does not protect a fundamental right to terminate a pregnancy. This will put an end to cases questioning whether a given set of abortion regulations constitute an "undue burden" on a woman's right to an abortion, but (as Ilya notes below) it will not put an end to abortion-related litigation.
One consequence of the Dobbs decision is that much abortion litigation will shift from federal to state court. Just because there is no right to abortion in the federal constitution does not mean there is no such right to be found under state constitutions. Just as (to take one example) the Ohio Supreme Court has concluded that the Ohio Constitution provides greater protection for private property against eminent domain than does the Fifth Amendment to the U.S. Constitution, state supreme courts may conclude that state constitutional provisions protect abortion rights through state-level rights to privacy (as in Montana) or other liberty-protecting provisions. Of course, such claims will not always be successful. The Iowa Supreme Court recently issued a state-level Dobbs decision, rejecting prior decisions that had recognized a state-level abortion right.
Many of the post-Dobbs legal fights over abortion will involve questions about the scope of federal and state power over abortion, such as whether states can limit the ability to cross state lines to obtain abortions or whether federal drug regulation constrains the ability of states to limit access to medication abortions.
