The stability of interfaces and the mechanisms of thin film growth on semiconductors are issues of central importance in electronic devices. These can be understood through detailed study of the relevant microscopic processes. Experimental studies are able to provide detailed, atomic-scale information for model systems. Theoretical analysis of experimental results in essential in explaining certain surprising observations and in providing guidance for optimizing conditions and methods of growth. We review recent theoretical work on the diffusion of adatoms, the structure of adsorbate monolayers, and their implications for growth on the Si and Ge(111) surfaces. The theoretical analysis consists of first-principles calculations of the total-energy and entropy factors for stable, metastable and saddle-point configuration. These calculations are supplemented by Monte Carlo simulations of simple models that afford direct contact with experimental observations.