Electrodiffusion – migration of charges in solutions (typically wa- ter) – is an extremely important process for science and technology. Bulk properties (those are not sensitive to boundary conditions) of ionic mixtures are a central topic of electrochemistry, and has been well studied based on the Poisson-Boltzmann theory back to 1920s documented by the Gouy-Chapmann theory and Debye-Hu ̈ckel theory as well as their improvements. Ion channel problems concern macro- scopic properties of ionic flow through nano-scale membrane channels with more specifics structures and with highly non-trivial boundary ef- fects (in fact, these physical quantities are nonlinear interacting with each other to affect the properties of channel functions). It is not surprising that ion channel problems exhibit more richer phenomena and, on the other hand, are much more challenging than studies of bulk property of ionic mixture. We will start with a short background of ion channels and a brief description of a primitive models – the Poisson-Nernst-Planck system – for ionic flow through ion channels. We then focus on a discussion of a general geometric singular perturbation framework together with special intrinsic structures of PNP systems for an analysis. More im- portantly, we will report a number of concrete results that are directly relevant to central topics of ion channel problems.