Reaction path methods provide a powerful tool for bridging the gap between electronic structure and chemical dynamics. Classical mechanical reaction paths may usually be understood in terms of the force field in the vicinity of a minimum energy path (MEP). When there is a significant component of hydrogenic motion along the MEP and a barrier much higher than the average energy of reactants, quantal tunneling paths must be considered, and these tend to be located on the corner-cutting side of the MEP. As the curvature of the MEP in mass-scaled coordinates is increased, the quantal reaction paths may deviate considerably from the classical ones, and the force field must be mapped out over a wider region, called the reaction swath. The required force fields may be represented by global or semiglobal analytic functions, or the dynamics may be computed "directly" from the electronic structure results without the intermediacy of potential energy functions. Applications to atom and diatom reactions in the gas phase and at gas-solid interfaces and to reactions of polyatomic molecules in the gas phase, in clusters, and in aqueous solution are discussed as examples.