We briefly introduce some latest results of our studies on related ion channel problems. We mainly focus on the dynamics of ionic flows through membrane channels via Poisson-Nernst-Planck models under different setups, particularly the internal dynamics, which cannot be detected via current technology. More precisely, the characterization of the nonlinear interplays between different physical parameters, particularly, boundary conditions, finite ion sizes, permanent charges, diffusion coefficients and channel geometry, is our main focus. This provides detailed information and better understandings for the ionic flow properties of interest.