Rate equation treatments of nucleation and growth are recapped, and co
mpared with recent kinetic Monte Carlo simulations and scanning tunnel
ing microscope experiments. New rate-diffusion models are developed to
describe (a) nucleation on point defects, with application to island
growth of nm-sized Fe and Co particles grown on calcium fluoride subst
rates; (b) nucleation and diffusion in finite (1 and 2D) deposits, app
lied to diffusion over, and the break-up of, multilayer deposits of Ag
/Ge(111) and Ag/Fe(110). A brief discussion of pattern formation in th
ese and similar systems is given.