In this tutorial review we show how the methods and techniques of computational chemistry have been applied to the understanding of the physical basis of the rate enhancement of chemical reactions by enzymes. This is to answer the question: Why is the activation free energy in enzyme catalysed reactions smaller than the activation free energy observed in solution? Two important points of view are presented: Transition State (TS) theories and Michaelis Complex (MC) theories. After reviewing some of the most popular computational methods employed, we analyse two particular enzymatic reactions: the conversion of chorismate to prephenate catalysed by Bacillus subtilis chorismate mutase, and a methyl transfer from S-adenosylmethionine to catecholate catalysed by catechol O-methyltransferase. The results and conclusions obtained by different authors on these two systems, supporting either TS stabilisation or substrate preorganization, are presented and compared. Finally we try to give a unified view, where a preorganized enzyme active site, prepared to stabilise the TS, also favours those reactive conformations geometrically closer to the TS. © 2004 Royal Society of Chemistry.