The semiclassical (classical path) method has over the years probably
been the most commonly used approximate method for describing many mol
ecular dynamical processes in inelastic, non-adiabatic and recently al
so in reactive scattering. Here an overview of the development of the
theory is given. Its connection to various other approximate dynamic t
heories such as the eikonal, time-dependent self-consistent field, Gau
ssian wave packet and the Feynmann path theory is discussed. Various n
umerical and technical schemes for solving the mixed quantum-classical
equations through algebraic, state and grid expansion methods are als
o given.