Group II introns are large, natural catalytic RNAs or ribozymes that were discovered in organelles of certain protists, fungi, algae, and plants and more recently also in prokaryotic organisms. In vitro, some members were found to self-splice from their pre-RNAs by two consecutive transesterification reactions joining the flanking exons and releasing the intron in a typical lariat form. Apart from self-splicing, a variety of other in vitro activities have been detected for group II introns demonstrating their amazing catalytic versatility. Group II introns fold into a conserved secondary structure consisting of six domains radiating from a central wheel that brings the 5' and 3' splice junction into close proximity. Domain 1 is the largest domain that is assumed to deliver the molecular scaffold assembling the intron in its active structure, while domain 5 is the phylogenetically most conserved part that represents the active site of the ribozyme. In vivo, the splicing reaction of many, if not all group II introns is assisted by proteins either encoded by the introns themselves (maturases), or encoded by other genes of the host organisms. The host proteins known to date have additional cellular functions and seem to have been adapted for splicing during evolution. Some of the protein-encoding group II introns were also shown to act as mobile genetic elements. They can integrate efficiently into intronless alleles of the same gene (homing) and at much lower frequencies into ectopic sites (transposition). The mobility process depends on intron encoded protein functions (endonuclease and reverse transcriptase) and on the intron RNA. This review provides a comprehensive survey of the structure/function relationships and the reaction potential of group II introns, the structurally most complicated, but also most fascinating ribozymes when looking at their catalytic repertoire in vitro and in vivo.