In general, complete mathematical modeling of electrical neurostimulation encompasses two separate problems; clear delineation of this article becomes important. Solutions are required for the time-varying macroscopic fields generated by the stimulating electrodes, and only then can biophysical analysis be brought to bear on neural structures within those fields. This article is focused on the second of these aspects, and provides a survey of mathematical representations including nerve cell bodies, myelinated and unmyelinated fibers of passage, branched systems, fiber terminals and composite neurons. Effects on nerve cells of fields generated by remote electrodes are given primary attention, although methods for obtaining field solutions in biological media are discussed in detail only where the issue is inextricably linked to the use of a particular neural model, or relates crucially to experimental validation. Within these guidelines, it is intended to show the significant role that current nerve cell models may play in attempts to understand mechanisms of neural stimulation, and in the development of more advanced strategies for electronic intervention and control of neural function.