What does Obergefell mean for Ohio divorce law?

On June 26, 2015, the United States Supreme Court issued its decision in the matter of Obergefell v. Hodges (576 U. S. 644 (2015)). In a 5-4 decision, the Court ruled that the Fourteenth Amendment requires states to issue marriage licenses to same-sex couples and recognize the marriage of same sex couples who were lawfully married in another state. In Ohio, which previously did not allow same-sex marriage, this meant not only a change in the laws surrounding marriage, but the laws surrounding divorce.