Thin films are structures consisting of one or several nanoscale atomic layers of material that are used to either functionalize a surface or constitute components in more complex devices. Many properties of a film are closely related to its microstructure, which allows films to be tailored to meet specific technological requirements. Atom-by-atom film growth from the vapor phase involves a multitude of atomic processes that may not be easily studied experimentally in real-time because they occur in small length- (? Å) and timescales (? ns). Therefore, different types of computer simulation methods have been developed in order to test theoretical models of thin film growth and unravel what experiments cannot show. In order to compare simulated and experimental results, the simulations must be able to model events on experimental time-scales, i.e. on the order of microseconds to seconds. This is achievable with the kinetic Monte Carlo (kMC) method. In this work, the initial growth stages of metal deposition on weakly-interacting substrates is studied using both kMC simulations as well as experiments whereby growth was monitored using in situ probes. Such film/substrate material combinations are widely encountered in technological applications including low-emissivity window coatings to parts of microelectronics components. In the first part of this work, a kMC algorithm was developed to model the growth processes of island nucleation, growth and coalescence when these are functions of deposition parameters such as the vapor deposition rate and substrate temperature. The dynamic interplay between these growth processes was studied in terms of the scaling behavior of the film thickness at the elongation transition, for both continuous and pulsed deposition fluxes, and revealed in both cases two distinct growth regimes in which coalescence is either active or frozen out during deposition. These growth regimes were subsequently confirmed in growth experiments of Ag on SiO2, again for both pulsed and continuous deposition, by measuring the percolation thickness as well as the continuous film formation thickness. However, quantitative agreement with regards to scaling exponents in the two growth regimes was not found between simulations and experiments, and this prompted the development of a method to determine the elongation transition thickness experimentally. Using this method, the elongation transition of Ag on SiO2 was measured, with scaling exponents found in much better agreement with the simulation results. Further, these measurement data also allowed the calculation of surface properties such as the terrace diffusion barrier of Ag on SiO2 and the average island coalescence rate. In the second part of this thesis, pioneering work is done to develop a fully atomistic, on-lattice model which describes the growth of Ag on weakly-interacting substrates. Simulations performed using this model revealed several key atomic-scale processes occurring at the film/substrate interface and on islands which govern island shape evolution, thereby contributing to a better understanding of how 3D island growth occurs at the atomic scale for a wide class of materials. The latter provides insights into the directed growth of metal nanostructures with controlled shapes on weakly-interacting substrates, including twodimensional crystals for use in catalytic and nano-electronic applications.