For further information, see Understanding the Federal Courts from the United States Courts.
The US Constitution, Article III, section 2 outlines the jurisdiction of the federal courts:
The jurisdiction of the highest US court is:
There are presently 13 different circuits. They review all final decisions and certain interlocutory decisions of district courts within their circuit, review decisions of the tax court, and review decisions of federal administrative boards.
Each state has one or more district courts, with the following jurisdiction:
These include Court of Federal Claims, Court of Appeals for the Federal Circuit, Tax Court, Court of International Trade, Court of Appeals for the Armed Forces, etc.