What court case established a three-part test to determine obscenity?

The court case that established a three-part test to determine obscenity is Miller v. California (1973). In this landmark decision, the Supreme Court outlined the "Miller Test," which assesses whether material is considered obscene based on community standards, whether it depicts sexual conduct in a patently offensive way, and whether it lacks serious literary, artistic, political, or scientific value. This framework has since been used to evaluate cases involving obscenity in the United States.