THE determination of mechanisms of enzyme action is among the great problems of modern chemistry (Boyer e t a l . , 1960; Boyer, 1960; Westheimer, 1959). Although not one enzymatic process is today understood, and although no model system has achieved catalytic activity comparable to that of the corresponding enzyme, considerable progress has been made in elucidating the "active sites" in enzymes, and in finding catalytic systems which will operate (although slowly) under experimental conditions which are comparable to those in cells and, hopefully, by mechanisms which parallel the biochemical ones. The problem is under attack from many angles: studies of peptide sequences, X-ray analysis of protein structure, determination of the coenzyme or active sites needed for reaction, kinetic studies of enzyme action, and chemical "models" for various enzymatic systems. All of these methods provide information relevant to the central problem; how does a protein strongly accelerate a chemical reaction between a substrate and either a coenzyme molecule or an active site on the protein itself or some other reagent. In subsequent sections of this review, some individual enzymes are considered in some detail. Before considering these systems, a few words might help set the problem in perspective. Much of our understanding of catalytic action has been gained by studies of model systems. The pioneers in such investigations (Langenbeck, 1935 ; Warburg 1949) did not have the present-day background of theoretical chemistry on which to build. In 1947, in a paper more pertinent to modern considerations of detailed mechanism, Braunstein suggested the outlines of a mechanism for transamination: this mechanism and the role of pyridoxal have been strongly substantiated (Braunstein, 1960; Metzler e t a l . , 1954; Ikawa & Snell, 1954) and are generally accepted today. More recently, the role of thiamin in the decarboxylation of pyruvate (Breslow, 1958), the action of diphosphopyridine nucleotides in the direct and stereospecific transfer of hydrogen (Vennesland & Westheimer, 1954), and the role of the serine residue in the reactions of esterases (Desnuelle, 1960a, b; Cohen e t a l . , 1959) and of phosphoglucomutase (Koshland & Erwin, 1957) have been discovered, and imitated with model systems. Some of these systems are here considered. The role of biotin and of several other coenzymes in enzymatic processes will be discussed in another session in this Congress. In a recent summary (Westheimer, 1959), the author stated, " . . . hopefully, in another decade, reviews may be concerned with enzymes and enzyme analogs (rather than with models) . . . ". The decade has not yet passed, and the prediction still seems reasonable.