The localization of neural electromagnetic sources from measurements at the head surface requires the solution of an inverse problem; that is, the determination of the number, location, spatial configuration, strength, and time-course of the neuronal currents that give rise to the magnetic field or potential distribution. In most general form, the neuromagnetic and electrical inverse problems are ill-posed and have no unique solution; however, approximate solutions are possible if assumptions are made regarding the shape and conductivity of the head and the number and configuration of neuronal currents responsible for the surface distributions. To help resolve ambiguities and to reduce the number and range of free parameters required to model complex neuromagnetic sources, the authors are investigating strategies to constrain the locations of allowable sources, based on a knowledge of individual anatomy. The key assumption, justified by both physiological evidence and theoretical considerations, is that the dominant neuromagnetic sources which contribute to surface field distributions reside within the cortex. It is demonstrated that anatomically constrained source modeling strategies can produce significant improvements in source localization; however, the conclusion is that additional improvements in model fitting or source reconstruction procedures are required.