Due to scientific and technological interest many studies are concerned with growth modes for the first monolayers of epitaxial growth. By combination of microscopy (like STM) and diffraction (like spot profile analysis of LEED) the important steps of film formation via deposition, migration, nucleation and film completion are studied. Temperature, deposition rate and defects of substrate and of the growing film drastically influence the growth modes in homoepitaxial systems with respect to island density, roughness or facet appearance. For heteroepitaxial growth the misfit and the surface energies are decisive for the growth mode. Depending on the type of bonding the growing film is more or less determined by the structure of the substrate. For metals on metals the film is more or less floating where only the orientation is provided by the substrate. For metals on semiconductors some influence on the lattice constant is seen, which depends on the temperature of deposition. For semiconductors on semiconductors a one-to-one correspondence of film atoms to substrate atoms requires a clear transition from pseudomorphic to relaxed growth of the film by dislocations at the interface. For accommodation to the substrate each film has to develop special defects, which depend both on the system and on the growth parameters. The wide variety of growth modes and some specific film defects are qualitatively demonstrated with STM images and quantitatively described by spot profile analysis of electron diffraction (SPA-LEED).