Polymer gels are commonly used in industrial, analytical, and domestic applications; their uses are likely to continue expanding as gels with novel chemical and structural characteristics are developed. These applications often rely on the precise control of the adsorption behavior of a gel. Development of useful gels, however, has been hampered by a lack of molecular-level understanding of the physics underlying phase transitions in such materials. In this report, we review recent molecular simulation work related to the study of fundamental aspects of network elasticity and of phase transitions in polymeric gels. In particular, simulations of simplified (coarse-grained) molecular models are described which provide insights into the general behavior of gels, as opposed to studies concerned with the properties of specific materials. Methodological aspects unique to the simulation of different properties of polymeric gels are emphasized. We also pay special attention to the role of entropic factors (such as network topology, backbone stiffness,, chain length asymmetry), over that of energetic interactions (such as hydrofobic interactions or ionic forces) on the onset and characteristics of phase transitions in gels. In spite of the important advances made over the fast years in methodology and computer hardware, many challenges remain if phase transitions for more realistic gel models are to be simulated. (C) 1999 Elsevier Science B.V. All rights reserved.