The use of wave packets in time-dependent quantum mechanical studies of chemical reaction dynamics is examined. The basic priniciples of time-dependent scattering theory are reviewed. The Fourier-grid method and various propagation schemes are discussed. A number of useful methodologies are examined, such as discrete variable representations and close-coupling expansions, multiconfiguration self-consistent field formulations, and the mixing of classical with quantum variables. Numerous applications to gas-surface scattering are considered. The dissociative adsorption of diatomic molecules on metal surfaces and the Eley-Rideal recombination of gas-phase atoms with atoms adsorbed on surfaces are discussed in detail. Applications to gas-phase reactions are also examined, with emphasis on three-body A + BC and four-body AB + CD reactions.