This review deals with enzymes where structures and kinetic studies have provided information on chemical mechanism and transition-state structure. Emphasis is put on nonenzymatic phosphate transfer, enzymatic phosphate transfer and sulfate transfer. Under nonenzymatic phosphate transfer, discussion covers uncatalyzed reactions of phosphomonoesters, reactions of phosphodiesters and implications for enzymatic catalysis. As for enzymatic phosphate transfer, emphasis is on phosphatases, regulatory enzymes, phosphoglucomutases, kinases, enzymes with a carboxyphosphate intermediate, transcarbomylases, ATPases and ATP synthesis, phosphodiesterases, nucleotidyltransferases and phosphotriesterase. With regards to sulfate transfer, topics discussed include types of sulfate esters, uncatalyzed reactions of sulfomonoesters, uncatalyzed reactions of sulfate diesters and enzymatic sulfuryl transfer from PAPS.