An introductory review of the central ideas in the kinetics of submono
layer and multilayer expitaxial growth is followed by a more detailed
discussion of some recent developments in the field. The concepts of a
critical island size, dynamical scaling of the island-size distributi
on, and the barrier to interlayer diffusion (Ehrlich-Schwoebel barrier
) are introduced. The results of kinetic Monte Carlo simulations of a
realistic model of submonolayer epitaxial growth are presented and com
pared with rate-equation analyses and recent experiments. We also pres
ent an analytical expression for the scaled island-size distribution a
s a function of the critical island size which agrees well with our si
mulations as well as with experiments. Our results provide a quantitat
ive explanation for the variation of the submonolayer island density,
critical island size, island-size distribution and morphology as a fun
ction of temperature and deposition rate found in recent experiments.
We also present the results of a realistic model for multilayer growth
which includes a finite barrier to interlayer diffusion. A method for
determining the Ehrlich-Schwoebel barrier based on a comparison of si
mulations with experimental results for the reflection high-energy ele
ctron diffraction intensity, surface width, layer densities, and surfa
ce morphology is discussed. In particular, we find that for Fe/Fe(100)
the interlayer diffusion barrier is significantly less than the activ
ation energy for diffusion on a flat terrace.