Submonolayer epitaxial growth is obtained by the deposition of less than a complete layer of atoms on a single crystal surface. It is of fundamental interest for industrial applications (e.g. in the semiconductor industry) as well as from the point of view of basic research. For example, it is known that nanometer-sized atomic structures (nanostructures) exhibit remarkable physical and chemical properties which can differ greatly from those of bulk matter. In order to investigate these properties, it is often necessary to create large quantities of well defined and possibly spatially ordered nanostructures. One way to achieve this result is self-organized growth where one deposits atoms on a clean crystalline surface and lets the growth process evolve freely. Here, nanostructures result from the atomic diffusion and aggregation processes taking place at the surface. Understanding the exact nature of these processes is of ongoing interest in the field of nanostructure growth. In this thesis we report about submonolayer growth experiments of the ferromagnetic transition metal cobalt. Cobalt was chosen because it exhibits remarkable magnetic properties. These experiments were performed in an ultra-high vacuum chamber and molecular beam epitaxy was used to grow the nanostructures. Observations of the surface were made using a variable-temperature scanning tunneling microscope (STM). In order to get a better understanding of the atomic processes happening at the surface, we developed two adapted computational simulation methods. Kinetic Monte-Carlo (KMC) simulations were used to get an atomistic picture of the surface while mean field rate equations were integrated numerically to yield cluster densities. We study the growth of cobalt on three different surfaces. By depositing Co on a clean Pt(111) crystal surface, we observe that the platinum surface reconstructs by forming star-shaped partial dislocations for sample temperatures above 180 K (-93°C). We also observe that island densities deviate from predictions of all known models towards higher values for these same temperatures. By simulation we are able to show that insertion of Co into the topmost platinum layer creates a repulsive network of dislocations. We show that these dislocations act as diffusion inhibiting barriers and thus influence the island density by constraining the free movement of atoms at the surface. We also show that the Co dimer and trimer diffuse on Pt(111) before dissociating and are able to extract corresponding activation barriers. We also study the deposition of Co on a Ru(0001) surface which shows a more conventional temperature dependence. By comparing simulation and experiment we extract all relevant diffusion activation barriers and show that at high temperatures the Co dimer and trimer dissociate. Finally, we investigate the growth of Co on the hexagonal boron nitride superlattice which forms on a Rh(111) surface. On this surface Co clusters form three-dimensional hemispherical dots. We show how the substrate corrugation influences diffusion of Co atoms and that clusters up to the size of the pentamer can diffuse. By simulation, we also extract the relevant migrations and desorption barriers.