A one-dimensional model of presynaptic calcium diffusion away from the membrane, with cytoplasmic binding, extrusion by a surface pump, and influx during action potentials, can account for the rapid decay of phasic transmitter release and the slower decay of synaptic facilitation following one spike, as well as the very slow decline in total free calcium observed experimentally. However, simulations using this model, and alternative versions in which calcium uptake into organelles and saturable binding are included, fail to preserve phasic transmitter release to spikes in a long tetanus. A three-dimensional diffusion model was developed, in which calcium enters through discrete membrane channels and acts to release transmitter within 50 nm of entry points. Analytic solutions of the equations of this model, in which calcium channels were distributed in active zone patches based on ultrastructural observations, were successful in predicting synaptic facilitation, phasic release to tetanic spikes, and the accumulation of total free calcium. The effects of varying calcium buffering, pump rate, and channel number and distribution were explored. Versions appropriate to squid giant synapses and frog neuromuscular junctions were simulated. Limitations of key assumptions, particularly rapid nonsaturable binding, are discussed.