The impact of charged-particles on the human’s life is constantly increasing, due to their importance in such domains as plasma physics, industrial processes, biology etc. It is related to a large variety of physical situations and has complex multiscale character. In this talk, I will explore the mathematical theory for the charged particles including the kinetic equations and continuum field models. In particular, I will discuss the diffusion limit of Vlasov-Poisson-Fokker-Planck (VPFP) equations to the Poisson-Nernst-Planck (PNP) equations for multispecies charged particles, which are widely used to describe the drift-diffusion of electrons and holes in semiconductors, as well as the movement of ions in solutions and protein channels. Besides, I will discuss the well-posedness and long-time behavior of the PNP equations with a nonlinear generation-recombination rate.