The talk will focus on applications from rigorous analysis of some Poisson-Nernst-Planck (PNP) type models for ion transport through membrane channels. Due to multi-variable and multi-scale features, and nonlinear interactions presented in the problem, the study demands a great deal of mathematical analysis efforts. The talk will start with a brief review of a geometric singular perturbation theory specified for analyzing PNP that has been developed based on modern geometric singular perturbation theory of nonlinear dynamical systems. The analysis allows one to track the nonlinear interplays between relevant physical quantities and to extract critical information on ionic flow properties, such as effects of ion sizes, permanent charges and channel geometry, at least, in simple settings.