Recent experimental advances have shown that enzymes are flexible molecules, and point to a direct link between dynamics and catalysis. Movements span a wide time range, from nano- to milli-seconds. In this paper we introduce two aspects of enzyme flexibility that are treated with two appropriate techniques. First, transition path sampling is used to obtain an unbiased picture of the transition state ensemble in chorismate mutase, as well as its local flexibility and the energy flow during the chemical step. Second, we consider the binding and release of substrates in L-rhamnulose-1-phosphate aldolase. We have calculated the normal modes of the enzyme with the elastic network model. The lowest frequency modes generate active site deformations that change the coordination number of the catalytic zinc ion. The coordination lability of zinc allows the binding and release of substrates. Substitution of zinc by magnesium blocks the exchange of ligands.