Mathematical models of neural networks now predict complex system behavior which mimics that seen in live brain tissue. These models are derived from basic membrane properties and connectivity patterns which have been determined by experimentation. In turn, the models make testable predictions about the behavior of the neural systems and about the properties of the individual neurons within the system. We will describe the collaboration between experimenters and theorists which produced our current understanding of the mechanisms of synchronous epileptic activity in the hippocampal slice preparation. We will consider first the measurement and computer modeling of the intrinsic biophysical properties of the pyramidal cells. We then go on to review the exploration and modeling of three mechanisms of interaction between neurons which produce synchronous epileptic activity: synaptic connections, electrotonic junctions, and electric fields. © 1985.