The talk is on mathematical analysis of primitive Poisson-Nernst-Planck (PNP) models for ionic flows through ion channels. Due to multi-variable and multi-scale features, and nonlinear interactions presented in the problem, the study necessarily demands a great deal of mathematical analysis efforts and, most likely, new mathematical theory. A geometric singular perturbation framework for analyzing PNP is developed based on advanced nonlinear dynamical systems theory of invariant manifolds and modern geometric singular perturbations. For applications of these general theory to PNP type models, special structures are revealed that allow more or less explicit characterizations of critical quantities for ionic flows in terms of parameters defining the problem. In turn, concrete information can be extracted from the analysis to provide direct, hopefully significant, insights for mechanisms of ionic flow properties.