Court of Criminal Appeals
After a trial court has decided a criminal case, the State or the defendant may appeal to a higher court.
The appeals of all cases in which the death penalty has been assessed come directly to the Court of Criminal Appeals from the trial courts. The appeals of all other criminal cases go to one of fourteen Courts of Appeals in Texas, and their decisions may be reviewed by the Court of Criminal Appeals. The Court also has sole authority to grant the writ of habeas corpus to a person who has been convicted of a felony (which is a crime that is punishable by death or by imprisonment in the Department of Criminal Justice).
See About Texas Courts for more information about the Texas Judiciary, which includes the Courts of Appeals and other parts of Texas' judicial system. There you will also find links to a pamphlet on the Texas Judicial System, in multiple formats.