The 1987 Lambeth conventions identify an arrhythmia from time series recordings of cardiac electrical activity. All cardiac arrhythmias are spatio-temporal and involve anisotropic and orthotropic propagation in heterogeneous tissue. Spatial heterogeneities are increased by infarction, or localised ischaemia. Spatio-temporal excitation on the surface of the heart can be reconstructed from body surface maps obtained by multi-channel ECG, and mapped in vivo by multi-electrode recording socks, or visualised optically using voltage sensitive dyes in isolated perfused tissue or whole hearts, at resolutions down to ∼0.2 mm and 0.5 ms. Computational models, based on cell electrophysiology, tissue heterogeneity from molecular mapping by immuno-histochemistry, quantitative PCR and mRNA expression, and tissue anisotropy and orthotropy from diffusion tensor magnetic resonance imaging for cardiac tissues of mouse, rabbit, guinea pig, dog and human are available for the interpretation and simulation in 3-D geometries of these spatiotemporal recordings. Spatial features of the surface activity can readily be mapped, for example, action potential duration (APD) and its restitution, discordant alternans, dominant frequencies and their domains, phase singularities that locate the organisation centres of re-entrant waves at the surface. Such spatial maps allow putative mechanisms for arrhythmias to be tested, for example, the mother rotor hypothesis for fibrillation. We present spatial maps we have obtained of APD, repolarisation time, discordant alternans, dominant frequencies and phase singularities during fibrillation obtained from optical imaging experiments (mouse, rat, guinea pig, rabbit and pig) and simulations (mouse, rat, rabbit, dog, human) and quantify the maps and their dynamics.