We review theoretical and simulational approaches to the description of equilibrium bulk crystal and interface properties as well as to the nonequilibrium processes of homogeneous and heterogeneous crystal nucleation for the simple model systems of hard spheres and Lennard-Jones particles. For the equilibrium properties of bulk and interfaces, density functional theories employing fundamental measure functionals prove to be a precise and versatile tool, as exemplified with a closer analysis of the hard sphere crystalliquid interface. A detailed understanding of the dynamic process of nucleation in these model systems nevertheless still relies on simulational approaches. We review bulk nucleation and nucleation at structured walls and examine in closer detail the influence of walls with variable strength on nucleation in the Lennard-Jones fluid. We find that a planar crystalline substrate induces the growth of a crystalline film for a large range of lattice spacings and interaction potentials. Only a strongly incommensurate substrate and a very weakly attractive substrate potential lead to crystal growth with a non-zero contact angle.