There are many types of active ion channel beyond the squid giant axon sodium and potassium voltage-gated ion channels studied in Chapter 3, including channels gated by ligands such as calcium. The aim of this chapter is to present methods for modelling the kinetics of voltage-gated and ligandgated ion channels at a level suitable for inclusion in compartmental models. The chapter will show how the basic formulation used by Hodgkin and Huxley of independent gating particles can be extended to describe many types of ion channel. This formulation is the foundation for thermodynamic models, which provide functional forms for the rate coefficients derived from basic physical principles. To improve on the fits to data offered by models with independent gating particles, the more flexible Markov models are introduced. When and how to interpret kinetic schemes probabilistically to model the stochastic behaviour of single ion channels will be considered. Experimental techniques for characterising channels are outlined and an overview of the biophysics of channels relevant to modelling channels is given.