This thesis is concerned with the molecular dynamics and rheology of polymer melts in the vicinity of a hard flat surface. One initial motivation is the desire to better understand the phenomenon of slip between flowing molten polymer and a bounding solid wall. Alternation between sticking and slipping boundary conditions is suspected to be the cause of 'spurt flow', widely observed in polymer extrusion. A related aim is to investigate the nature of chain entanglements at surfaces, which also has important consequences for the material properties of nano-composites and thin films. In addition more general effects of confinement are considered. The primary method of investigation is observation, using Molecular Dynamics (MD) computer simulations of relevant systems. Single-chain models are fitted to the 'fundamental' multi-chain MD simulations, and the simplifying assumptions of this coarse-graining are then examined.