Thin-films are used in a variety of applications ranging from semiconductor technology to industrial coatings, sensors, and photovoltaic devices. In addition, understanding thin-film growth is a challenging scientific and technical problem which requires an understanding of surface and interface physics. After a brief review of some applications, I will discuss some new simulation techniques, including the kinetic Monte Carlo method as well as temperature-accelerated dynamics (TAD) and parallel TAD (parTAD) which have allowed us to make substantial progress. I will then discuss the application of these methods to study submonolayer and multilayer metal epitaxial growth. In particular, the results of simulations we have carried out in order to understand strain relaxation and “vacancy” formation in low-temperature Cu/Cu(100) growth as well as the effects of strain on island-shape in submonolayer Cu/Ni(100) growth, will be discussed. If time permits, recent simulations and density-functional theory calculations which we have carried out to explain the non-monotonic temperature-dependence of the roughness in multilayer Ag/Ag(100) growth will also be discussed. In general, we find that thin-film growth is a surprisingly complex process which typically involves a competition between a variety of different and sometimes previously unexpected, atomic relaxation mechanisms. In addition, other effects such as the short-range attraction of depositing atoms to the substrate and shadowing can also play an important role. These results, as well as the wide range of rates and time-scales involved, indicate that the continued development of accurate and efficient multiscale simulation methods is likely to continue to play an important role in improving our understanding of thin-film growth.