Both cardiac and brain bioelectric forward problems can be modeled accurately as quasi-static, implying that torso or scalp surface measurements depend on the spatial distribution of the respective sources independently at each time instant. However in both cases the time courses of the sources are in large part a function of intrinsic electrophysiological dynamics, and so exhibit strong and complex temporal correlations. This suggests that it would be advantageous to incorporate temporal models into inverse methods, especially in light of the ill-posed nature of both problems. This talk will present some ideas, results, and possibilities for dynamic modeling in inverse bioelectric problems, concentrating primarily on electrocardiography. We will review some standard methods and describe how three such approaches are related through their assumptions about spatiotemporal covariance structure. We will then present some recent results with clinically measured data using a new method which incorporates a non-linear temporal model. Finally we will illustrate manifold-inspired, non-linear dynamic structure in measured signals, suggesting the potential for even more powerful dynamic modeling in the near future. If time permits we will also show results of our dynamic modeling of EEG and pose some questions about their implications for brain source localization.