The neural circuitry generating lamprey undulatory swimming is among the most accessible and best known of the vertebrate neuronal locomotor systems. It therefore serves as an experimental model for such systems. Modeling and computer simulation of this system was initiated at a point when a significant part of the network had been identified, although much detail was still lacking. The model has been further developed over 10 years in close interaction with experiments. The local burst generating circuitry is formed by ipsilateral excitatory neurons and crossed reciprocal inhibitory neurons. Early models also incorporated an off-switch lateral interneuron (L), the connectivity of which suggested it could contribute to burst termination at moderate to high bursting frequencies. Later examination of this model suggested, however, that the L interneuron was not of primary importance for burst termination, and this was later verified experimentally. Further, early models explained the effects of 5-HT on bursting frequency, spike frequency, and burst duration as being due to its modulatory action on the spike frequency adaptation of lamprey premotor interneurons. In current network models, accumulated adaptation is in addition the main burst terminating factor. Drive-related modulation of adaptation is explored as a mechanism for control of burst duration. This produces an adequate burst frequency range and a constant burst proportion within each cycle. It further allows for hemisegmental bursting, which has been observed experimentally. The local burst generator forms the basis of a network model of the distributed pattern generator that extends along the spinal cord. Phase constancy and flexibility of intersegmental coordination has been studied in such a simulated network. Current modeling work focuses on neuromodulator circuitry and action, network responses to input transients, how to model the intact versus an isolated piece of spinal cord, as well as on improving an earlier neuromechanical model of lamprey swimming.