[en] A program of research in Stellarator Transport Theory is described, with emphasis on kinetic modeling of divertor plasmas. We have developed a very efficient numerical solution of the kinetic equation. It was implemented first for the ions, self-consistently with the electrostatic potential, Φ, assuming quasineutrality and a Boltzmann distribution of electron density. The presheath problem has been solved, confirming analytic work in the collisionless limit and extending the earlier work to collisional cases. The effect of a transverse electric field on divertor flows in IMS is to redistribute the diverted flux. We have shown (experimentally) that rvec E x rvec B drifts are responsible. We thus used the 'presheath' model to examine the effect of magnetic mirrors along a diverted field line, both on the diverted fluxes and on the electrostatic potential. The calculated variation ΔΦ ∼ O(T_e) can be expected to set up significant flows. Numerical calculations of the stellarator ambipolar electric field and bootstrap current have been done. Further analytical and computational work on ripple transport is under way, in conjunction with IPP-Garching and as part of the US-USSR collaboration. Our earlier analytic calculations of stellarator ripple transport have also been modified to apply to tokamaks. 11 refs., 5 figs