Computational models of human atrial cells, tissues and atria have been developed. Cell models, for atrial wall, crista terminalis, appendage, Bachmann's bundle and pectinate myocytes are characterised by action potentials, ionic currents and action potential duration (APD) restitution. The principal effect of the ion channel remodelling of persistent atrial fibrillation (AF), and a mutation producing familial AF, was APD shortening at all rates. Electrical alternans was abolished by the modelled action of Dronedarone. AF induced gap junctional remodelling slows propagation velocity at all rates. Re-entrant spiral waves in 2-D models are characterised by their frequency, wavelength, meander and stability. For homogenous models of normal tissue, spiral waves self-terminate, due to meander to inexcitable boundaries, and by dissipation of excitation. AF electrical remodelling in these homogenous models led to persistence of spiral waves, and AF fibrotic remodelling to their breakdown into fibrillatory activity. An anatomical model of the atria was partially validated by the activation times of normal sinus rhythm. The use of tissue geometry from clinical MRI, and tissue anisotropy from ex vivo diffusion tensor magnetic resonance imaging is outlined. In the homogenous model of normal atria, a single scroll breaks down onto spatio-temporal irregularity (electrical fibrillation) that is self-terminating; while in the AF remodelled atria the fibrillatory activity is persistent. The persistence of electrical AF can be dissected in the model in terms of ion channel and intercellular coupling processes, that can be modified pharmacologically; the effects of anatomy, that can be modified by ablation; and the permanent effects of fibrosis, that need to be prevented.