Under the US Constitution, the highest court is the Supreme Court. The role of the Supreme Court is to hear the following: lawsuits between two or more states, cases concerning "ambassadors and other public ministers," cases of appeal, and any cases questioning a point of "constitutional and/or federal law" (United States Courts, "About the Supreme Court"). The Constitution grants Congress the power to oversee the Supreme Court, and over the years, the number of seats on the court has changed. The Judiciary Act of 1837 established the nine seats held today, including the chief justice and eight associate justices (Federal Judicial Center, "The Supreme Court of the United States and the Federal Judiciary").
The 13 U.S. Courts of Appeal count as the second type of U.S. courts. If a defendant does not think the decision handed by a district court was correctly guided by the law, the defendant has the right to appeal to the appellate court of the defendant's district. The role of the appellate courts is to decide "whether or not the law was applied correctly in the trial court" (United States Courts, "Court Role and Structure").
The third type of court is the district court, also called the trial court. Each state has "at least one district court," and there are a total of 94 U.S. District Courts across the nation ("Court Role and Structure"). Nearly all criminal and civil cases are heard by the district courts before being appealed to higher courts, should a case be appealed. In district courts, judges have the right oversee jury trials and sometimes to try cases without a jury. District court judges decide on the following "questions of law":
... the admissibility of certain kinds of evidence, the scope of a search warrant, or the legality of an arrest. (Georgia Tech, "Federal District Courts")
District courts will decide if, beyond reasonable doubt, a defendant committed a crime.
The primary difference between federal district courts and state district courts concerns the types of cases the courts can hear. State courts can hear almost any case concerning state laws and state citizens. Cases include "robberies, traffic violations, broken contracts, and family disputes" ("Federal vs. State Courts--Key Differences"). The only kinds of cases state district courts cannot hear concern federal crimes, "antitrust, bankruptcy, patent, copyright, and some maritime cases," which are all instead heard by federal district courts, in addition to any cases concerning the United States ("Federal vs. State Courts").