Many chemical and biological processes require the breaking and forming of chemical bonds and other quantum mechanical effects. Such processes cannot be simulated with standard classical molecular dynamics methods and require quantum mechanical methods. In many cases, the systems are so large that fully quantum mechanical calculations are not computationally practical. Such systems can be simulated using hybrid quantum/classical methods, which treat only the key regions quantum mechanically. This talk will provide an overview of hybrid quantum/classical computer simulations of chemical and biological processes. Three different types of simulations will be discussed. The first topic is mixed quantum mechanical/molecular mechanical free energy simulations of enzymes and ribozymes, which are RNA enzymes. The reactive region is treated with a quantum mechanical method such as density functional theory to allow bonds to form and break, while the remainder of the system is treated with standard classical molecular mechanical force fields. The multidimensional free energy surface is simulated with statistical methods that focus on the regions of interest. The second topic to be covered is nonadiabatic molecular dynamics simulations of photoinduced electron and proton transfer reactions. The excited electronic states of the molecule are calculated on-the-fly with a multiconfigurational quantum mechanical method during the molecular dynamics trajectory, while the solvent is treated with a molecular mechanical force field. Nonadiabatic transitions between the excited electronic states are included with a time-dependent quantum mechanical algorithm to simulate the relaxation process following photoexcitation. The third topic to be covered is electronic structure calculations of molecular systems that exhibit nuclear quantum effects and non-Born-Oppenheimer effects. Specified protons must be treated quantum mechanically on the same level as the electrons in order to calculate accurate molecular properties. Supercomputers have been essential to the success in all three of these areas.