[en] Fusion reactors based on the Tokamak concept (possibly mirrors, too) will require a low energy method of fueling. Refueling by using solid pellets of hydrogen isotopes appears to be the most promising low energy technique. The main issue in assessing the feasibility of pellet fueling is the ability of the pellet to penetrate into the central region of the reactor. A review is presented of the various theories predicting the lifetime of the pellet and their regions of applicability. Among the phenomena considered are neutral ablation of the solid, ionized ablation of the solid, shielding of the pellet by neutral molecules and electrons and ions, flow of the ablation cloud, distortion of the magnetic field by the flow of an ionized ablation cloud, and charging and electrostatic shielding of the pellet. A brief summary of results of experiments done by the University of Illinois-Oak Ridge and Riso groups is presented. The results of these experiments indicate that, at least at the low temperatures and densities used, a neutral ablation-neutral shielding model is correct. Finally, since all indications are that in order for pellet fueling to be successful, high velocity pellets will be needed, a brief discussion of possible acceleration techniques is presented