The Federal government has jurisdiction throughout the United States its Territories and Possessions for the enforcement of Federal Law. Different Federal agencies may have specific types of Federal Laws that they enforce (customs, borders, counterfeiting, fugitives, drugs, immigrations, terrorism), or enforce laws on Federal Property (National Parks, Military Bases, Federal Buildings, Federal Lands, Indian Reservations, ect.) The FBI handles the most serious violation of Federal Law, and crimes committed on Federal property.
State Police; enforce state laws throughout their state, primarily on state roads, state lands, and serious or multi jurisdictional crimes.
County Sheriffs; have jurisdiction primarily within their county, and are the primary law enforcement in unincorporated areas.
City Police; are the primary law enforcement agency for incorporated cities.
There are State Courts and Federal Courts, each had jurisdiction over violations committed within or under there jurisdiction. Each has trial courts, appeals courts, and supreme courts, with the US Supreme Court being the highest court. State crimes are heard in the state system and can only move into the federal appeals system if there is an alleged violation of federal (Constitutional) protection. A party who wants that court to review a decision of a federal or state court files a "petition for writ of certiorari" in the Supreme Court.