Ion channels are formed by specific proteins embedded in the cell membrane and provide pathways for fast and controlled flow of selected ions down their electrochemical gradient. This activity generates action potentials in nerves, muscles and other excitable cells, and forms the basis of all movement, sensation and thought processes in living beings. While the functional properties of ion channels are well known from physiological studies, lack of structural knowledge has hindered development of realistic theoretical models necessary for understanding and interpretation of these properties. Recent determination of the molecular structures of potassium and mechanosensitive channels from x-ray crystallography has finally broken this impasse, heralding a new age in ion channel studies where study of structure-function relationships takes a central stage. In this paper, we present a critical review of various approaches to modelling of ion transport in membrane channels, including continuum theories, Brownian dynamics, and classical and ab initio molecular dynamics. Strengths and weaknesses of each approach are discussed and illustrated with applications to some specific ion channels.