An introductory review of the central ideas in the kinetics of multilayer epitaxial growth is presented. A realistic model for multilayer homoepitaxial growth on fcc(100) and bcc(100) surfaces which takes into account the correct crystal structure is discussed. The effects of instabilities which lead to mound formation and coarsening are discussed, and a unified picture of the effects of attractive and repulsive interactions at ascending and descending steps on surface morphology and island nucleation is presented. An accurate prediction of the observed mound angle for Fe/Fe(100) deposition is obtained analytically and by kinetic Monte Carlo simulations. The general dependence of the mound angle and mound coarsening behavior on the temperature, deposition rate and strength of the step barrier in bcc(100) and fcc(100) growth is also presented, and compared with recent experiments.