This talk is about a class of particle systems in which energy exchange among particles is mediated by "the environment", symbolized by a lattice of rotating disks in mechanical models and "energy tanks" in stochastic versions of these models. A number of years ago, J-P Eckmann and I studied models of this type. Taking for granted mathematical issues such as existence and uniqueness of NESS, local thermal equilibria etc., we derived formulas for energy and particle density profiles for chains coupled to unequal heat baths, and demonstrated agreement with numerical simulations. I have since revisited the analytical issues set aside in this earlier work, and have obtained partial resolution for certain stochastic models. In this talk, I will review earlier work and report on recent results.