Each state’s constitution and laws establish the state’s courts, which interpret state laws (and generally not federal laws). A court of last resort, often known as a supreme court, is usually the highest court in the state. Some states also have an intermediate court of appeals. Below these intermediate courts of appeal are the state trial courts, where most lawsuits begin. State trial courts are referred to differently in different states—often as district courts, circuit courts, or superior courts.

State courts are often courts of general jurisdiction—meaning they hear all types of cases—involving criminal law, family law, probate law, and general disputes involving money and property. But more populated counties often have courts of specific jurisdiction, such as family courts that only hear family law matters (divorce, child custody, child support); criminal courts that only hear criminal matters; and probate courts that only handle the probate of estates and related litigation.

In New Mexico, the state court system is structured with the New Mexico Supreme Court serving as the court of last resort. It is the highest appellate court in the state and has discretionary appellate jurisdiction over cases from lower courts. Below the Supreme Court is the New Mexico Court of Appeals, which is an intermediate appellate court that reviews decisions from the lower courts, except for those cases that go directly to the Supreme Court. At the trial level, New Mexico has District Courts, which are courts of general jurisdiction and handle a wide range of cases including criminal, civil, juvenile, and family law matters. These District Courts are present in each of the state's 33 counties and are where most lawsuits begin. In addition to these, New Mexico also has Magistrate Courts and Municipal Courts, which are courts of limited jurisdiction. Magistrate Courts handle smaller civil cases, misdemeanors, and traffic violations, while Municipal Courts deal with municipal ordinance violations. For specific matters, such as probate cases, there are also Probate Courts in each county, although their jurisdiction is limited to certain types of cases involving the probate of estates.