Group I and group II introns are two types of RNA enzymes, ribozymes, that catalyze their own splicing by different mechanisms. In this review, we summarize current information about the structures of group I and group II introns, their RNA-catalyzed reactions, the facilitation of RNA-catalyzed splicing by protein factors, and the ability of the introns to function as mobile elements. The RNA-based enzymatic reactions and intron mobility provide a framework for considering the role of primordial catalytic RNAs in evolution and the origin of introns in higher organisms.