Catalysis fulfills the promise that high-yielding chemical transformations will require little energy and produce no toxic waste. This message is carried by the study of the evolution of molecular catalysis of some of the most important reactions in organic chemistry. After reviewing the conceptual underpinnings of catalysis, we discuss the applications of different catalysts according to the mechanism of the reactions that they catalyze, including acyl group transfers, nucleophilic additions and substitutions, and C-C bond forming reactions that employ umpolung by nucleophilic additions to C=O and C=C double bonds. We highlight the utility of a broad range of organocatalysts other than compounds based on proline, the cinchona alkaloids and binaphthyls, which have been abundantly reviewed elsewhere. The focus is on organocatalysts, although a few examples employing metal complexes and enzymes are also included due to their significance. Classical Bronsted acids have evolved into electrophilic hands, the fingers of which are hydrogen donors (like enzymes) or other electrophilic moieties. Classical Lewis base catalysts have evolved into tridimensional, chiral nucleophiles that are N- (e.g., tertiary amines), P- (e.g., tertiary phosphines) and C-nucleophiles (e.g., N-heterocyclic carbenes). Many efficient organocatalysts bear electrophilic and nucleophilic moieties that interact simultaneously or not with both the electrophilic and nucleophilic reactants. A detailed understanding of the reaction mechanisms permits the design of better catalysts. Their construction represents a molecular science in itself, suggesting that sooner or later chemists will not only imitate Nature but be able to catalyze a much wider range of reactions with high chemo-,regio-, stereo-and enantioselectivity. Man-made organocatalysts are much smaller, cheaper and more stable than enzymes.