Appeals can be either discretionary or of right. An appeal of right is one that the higher court must hear, if the losing party demands it, while a discretionary appeal is one that the higher court may, but does not have to, consider. For example, in the federal system, there is an appeal of right from the District Court to the Court of Appeals, but appeals from the Court of Appeals to the Supreme Court are discretionary.
Appeals do not always originate from court decisions. In administrative law, people are often allowed to appeal, in court, the decisions made by executive agencies.