The Boltzmann equation, which is central to the description of many linear and nonlinear transport processes, is the equation of an ideal gas of point molecules. The Enskog equation was proposed to model the finite diameter of molecules of real gases, but does not include the effects of intermolecular potentials. We describe some models which include a finite range approximation of such intermolecular potentials. In particular, we outline the existence of weak global-in-time solutions for a kinetic equation with piecewise constant intermolecular potential.