Recent determination of the molecular structures of potassium andmechanosensitive channels from x-ray crystallography has led to arenewed interest in ion channels. The challenge for permeation modelsis to understand the functional properties of channels from the availablestructural information. Here we give a critical review of the three maincontenders, namely, continuum theories, Brownian dynamics and moleculardynamics. Continuum theories are shown to be invalid in a narrow channel environment because they ignore the self-energy of ions arising from theinduced charges on the dielectric boundary. Brownian and moleculardynamics are thus the only physically valid methods for studying thestructure-function relations in ion channels. Applications of thesemethods to potassium and calcium channels are presented, which illustratethe multi-ion nature of the permeation mechanism in selective biologicalchannels.