The effect of spatial gradients, whether associated with surfaces or otherwise, on charged particle phase-space distribution functions and transport properties is a long-standing problem in the kinetic theory of gases. This article first discusses the necessary ingredients for an accurate kinetic theory analysis of the space–time behavior of electrons in gases and compares the different approaches currently in use. We then focus upon the electrons in a radio-frequency discharge away from the walls, where gradients are weak, and point out that the fundamental kinetic theory of even the boundary-free problem still warrants more careful attention than has been given to it in much of the contemporary literature. We highlighted the importance of careful analysis by presenting results for the first comprehensive “multiterm” solution of Boltzmann’s equation furnishing the complete set of hydrodynamic transport coefficients for electrons in an ac field undergoing ionization and attachment.