Eukaryotic membranes control dynamic intracellular signalling. (a) Massive diversification of lipids and ion channels creates compartments and circuits within a flexible and excitable endomembrane system. (b) The mitochondrion has a distinctive two-layer topology with unique capacitative properties (IM, inner membrane; OM, outer membrane; Ci, Co are IM, OM capacitances; Ri, Ro and Rm are IM, OM and matrix resistances; Rs is the resistance of the inner membrane space; Rc is a ‘shunt’ resistance [264] arising from cristae extending across the intermembrane space). (c) Excitable signalling in cilia manifests as fast transitions or escape responses, as observed here in an octoflagellate protist [228] which switches between three distinct behavioural states (run, stop and shock).