From a single chain in a dilute solution to an entangled polymer melt, from bulk systems to more complex interfacial problems, computer simulations have played a critical role not only in testing the basic assumptions of various theoretical models but also in interpreting experimental results. Early computer simulations of polymers were mostly carried out on a lattice using Monte Carlo methods. This approach has led to significant progress in recent years and will continue to do so in many areas. In some cases however, for example in the study of shear, lattice models have serious limitations. For this reason and also due to the availability of more powerful computers, continuum, off-lattice polymer models have recently become popular. In this article, we review some of the recent progress in studying polymers at surfaces and interfaces using continuum models.