This review considers the advances made in using computer simulations to elucidate the catalytic power of enzymes. It is shown that some current approaches, and in particular the empirical valence bond approach, allow us to describe enzymatic reactions by rigorous concepts of current chemical physics and to estimate any proposed catalytic contribution. This includes evaluation of activation free energies, nonequilibrium solvation, quantum mechanical tunneling, entropic effects, and other factors. The ability to evaluate activation free energies for reactions in water and proteins allows us to simulate the rate acceleration in enzymatic reactions. It is found that the most important contribution to catalysis comes from the reduction of the activation free energy by electrostatic effects. These effects are found to be associated with the preorganized polar environment of the enzyme active site. The use of computer simulations as effective tools for examining different catalytic proposals is illustrated by two examples. First, we consider the popular proposal that enzymes catalyze reactions by special dynamical effects. It is shown that this proposal is not supported by any consistent simulation study. It is also shown that the interpretation of recent experiments as evidence for dynamical contributions to catalysis is unjustified. Obviously, all chemical reactions involve motion, but unless this motion provides non-Boltzmann probability for reaching the transition state there are not dynamical effects. Vibrationally enhanced tunneling is shown to be a well understood phenomenon that does not lead to special catalytic effects. Similarly, it is shown that nonequilibrium solvation effects do not constitute dynamical contributions to catalysis. Second, the effectiveness of simulation approaches is also demonstrated in studies of entropic contributions to catalysis. It is found that the corresponding contributions are smaller than previously thought.