In a reactor grade device, the role of core fueling is to replace the D and T consumed in the fusion reactions (almost negligible) and to compensate the plasma losses through the separatrix -including the material expelled out by the ELMs. For this purpose, deep material deposition is an advantage and pellet injection the best candidate for fueling the future machines. Fueling by pellet injection consists in two phases: First, the pellet ablation itself, then the ablated material homogenization and drift in the discharge. The former is a self-regulated process, which depends only of the local plasma characteristics. The second is a global phenomenon, which depends on the whole magnetic configuration. In this paper, we discuss first the basics of the ablation physics, emphasizing the role of the fast particles -ions and electrons -resulting from NBI or wave heating; then we describe the homogenization process and associated ∇B-induced drift. The drift acceleration and damping processes are described as well as the influence of the magnetic configuration (tokamak, stellarator and reversed field pinch) on the predominance of a given damping process and its consequence on the resulting deposition profile. We finally review the last results relative to pellet fueling in these different kind of devices and present the ongoing projects for future large-scale machines.