In both state and federal courts, there are trial courts, where cases are first heard, and appellate or “higher” courts, which review decisions from trial courts. To appeal a case means to petition an appellate court to overturn or modify a decision of the trial or “lower” court. (See Appealing a Conviction and Criminal Writs.)
In the state systems, the names of criminal courts vary greatly from state to state. In some, the lowest level of criminal courts go by names like magistrate courts, police courts, or traffic courts. (They often hear bail motions and arraignments.) The next level of courts may be called municipal courts, superior courts, or county courts—these are trial courts. Many courts have their own appellate divisions—such divisions may, for example, hear only appeals of misdemeanor and infraction cases. Then there’s usually an intermediate appellate court (for example, the California Courts of Appeal), and then the highest court, often called the supreme court (for example, the California Supreme Court).
While state courts process most criminal cases, federal courts handle an increasing number of crimes, including those occurring on federal property and those taking place in more than one state (such as interstate drug trafficking). (See State vs. Federal Prosecution.)
The federal system comprises (in order of hierarchy):