Epitaxial growth encompasses processes and phenomena in which atoms are deposited on the surfaces of crystals. This talk addresses aspects of the following question. How can the random motion of atoms on the lattice of such surfaces give rise to organized nanoscale structures? We will discuss recent progress and open challenges in this direction. By starting with descriptions of atomistic dynamics in 1+1 dimensions, we will formally show the emergence of a deterministic model for the motion of nanoscale line defects, steps, on the crystal surface.