Some Supreme Courts only decide on constitutional issues, or if someone believes a constitutional right has been denied. It depends on the country. Some countries' Supreme Courts also examine all cases submitted, but, if the Brazilian example serves, it can take many years for a case to be seen. Pushing up criminal cases is a common strategy to exhaust the time window in which a case can be prosecuted.
These are usually referred to as constitutional courts. Because the Constitution vests "the judicial Power of the United States" in "one supreme Court," ours is also the court of final appeal.