Abstract: Protein channels are macromolecules with holes down their middle that span the membranes of biological cells. They control almost all ionic flow into and out of cells and thus govern an enormous range of physiological function important in health and disease.

In this talk I'll review the basic experimental knowledge on ion flow through these proteins and describe mathematical modelling approaches that aim to explain and predict the (biological) function of these channels given their structure. Interesting connections to the theory of stochastic processes and to non-equilibrium statistical mechanics will be described as well as some theoretical open questions.