Each of our judicial (state and federal) have a hierarchy of courts. In State Courts, California in particular, there are 3 levels of State Courts – the Superior Courts (Limited and Unlimited) which is where all civil suits start and are called “trial courts”; each county has a group of Superior Courts. Then the Court of Appeals which is broken up by Regions, are the courts that hear appeals on rulings from the Superior Courts in their region. From the Court of Appeals is the California Supreme Court which hears appeals on rulings made from the Court of Appeals throughout the entire State. If your case is heard in front of the California Supreme Court and either party is unhappy with the outcome, then the dissenting party can petition to be heard by the Supreme Court of the United States. (which according to the SCOUS website, the Supreme Court receives approximately 10,000 petitions to be heard each year and they only accept between 75 to 80!). Anyone can appeal a ruling, the further up the chain you go, the more unlikely it will be heard by the Court unless the issue is of “great public importance”.
Limited Case Appeals from the Superior Court are heard by the Appellate Court that is typically housed in the main Superior Court of the County; Unlimited case appeals are heard by the Court of Appeals (which is housed in State Courthouse). For example, Contra Costa Country Unlimited Appeals are heard by the Court of Appeals in San Francisco. For more details on the structure of the California State Courts see Overview of Courts.