State supreme courts are the highest judicial authority within each U.S. state. They primarily handle appeals from lower courts, ensuring that state laws are interpreted and applied correctly. Each state has its own supreme court, which may consist of a varying number of justices, typically ranging from five to nine. These courts play a crucial role in shaping state law and can address significant legal issues, including constitutional matters. Their decisions are final unless a case is taken to the U.S. Supreme Court, which only occurs in specific circumstances involving federal law or constitutional questions.