Many of the fundamentals of epitaxial growth, long predicted by theories of crystal growth, have been seen during the molecular beam epitaxial growth of monolayer films. In general, high temperatures and low deposition flux favor nucleation at atomic steps. The opposite extreme of low temperature and high flux favors island nucleation in terraces, and steps play little role. For intermediate conditions a wide variety of growth morphology is seen. High temperatures and high flux have been seen to produce two-dimensional dendritic growth. Atomic steps on substrates have been observed to migrate during sublimation. Pinning of steps during migration gives rise to complex atomic step and terrace structures and a distribution of terrace widths. For terraces wider than the diffusion length of adsorbed atoms, nucleation of islands is favored in the terraces, whereas narrow terraces favor nucleation at the atomic steps. For a constant substrate temperature and deposition flux, morphology can vary profoundly depending upon local terrace width. Complex structures in monolayer films are produced during sublimation. These include lockeime or hole nuclei which are one atomic step deep. Steps are seen to oscillate during step flow apparently due to considerable mass transport between steps and terraces.