The notion of local (dynamical, thermal, and chemical) equilibrium at fluid/solid interfaces which are the site of interesting nonequilibrium processes has proven useful to engineers for nearly a century and provides the basis for widely used methods described in textbooks on Transport Processes. Indeed, continuity of tangential velocity ("no-slip"), temperature, and species chemical potential are usually treated as "commandments", rather than often-useful approximations! However, in many current and emerging applications this class of approximations becomes unacceptable for easily understood reasons. We illustrate this here for ideal gas/solid interfaces across which, or tangent to, there are nonzero molecular fluxes of momentum, energy, and/or species mass. We make use of the concept of a Knudsen sublayer, at most several gaseous mean-free paths thick, inevitably present adjacent to the solid surface. While many scientific aspects of these phenomena have been known since the earliest studies of J. C. Maxwell (1879), we show that their engineering importance is now such that their understanding should be part of the education of all chemical engineers. Moreover, molecular-level numerical techniques can now be brought to bear to illuminate the nature of these near-interfacial regions, under more realistic nonequilibrium circumstances. Analogous phenomena occur in dense vapor/solid and liquid/solid cases. Such systems, far less well understood theoretically, are characterized by effects which are smaller numerically but which may still be quite exploitable (as for separations (Giddings, 1991; Caldwell, 1988)).