Neurons carry out the many operations that extract meaningful information from sensory receptor arrays at the organism's periphery and translate these into action, imagery and memory. Within today's dominant computational paradigm, these operations, involving synapses, membrane ionic channels and changes in membrane potential, are thought of as steps in an algorithm or as computations. The role of neurons in these computations has evolved conceptually from that of a simple integrator of synaptic inputs until a threshold is reached and an output pulse is initiated, to a much more sophisticated processor with mixed analog-digital logic and highly adaptive synaptic elements.