Ribozymes are folded catalytic RNA molecules that perform important biological functions. Since the discovery of the first RNA with catalytic activity in 1982, a large number of ribozymes have been reported. While most catalytic RNA molecules act alone, some RNA-based catalysts, such as RNase P, the ribosome, and the spliceosome, need protein components to perform their functions in the cell. In the last decades, the structure and mechanism of several ribozymes have been studied in detail. Aside from the ribosome, which catalyzes peptide bond formation during protein synthesis, the majority of known ribozymes carry out mostly phosphoryl transfer reactions, notably trans-esterification or hydrolysis reactions. In this review, we describe the main features of the mechanisms of various types of ribozymes that can function with or without the help of proteins to perform their biological functions.