During the last decade, ionospheric F region modeling has reached an accurate climatological level. We now have global computer models of the F region which simulate the interactions between physical processes in the ionosphere. Because of their complexity, these climatological models are confined to modern day supercomputers. This review focuses on the development and verification of these physical ionospheric models. Such models are distinct from local models, steady state models, and empirical models of the ionosphere, which are, by their conception, unable to represent physically the range of F region variability or storm dynamics. This review examines the limitations of the physical models, which are at the present time mainly associated with inputs to the ionospheric system. Of these, the magnetospheric electric field and auroral precipitation are by far the most dominant and yet the least well-defined dynamic inputs. Several developments are currently under way which could well lead to meteorological modeling capabilities in the next decade. For this the use of higher-resolution inputs, both temporal and spatial (for example, auroral imagery), is critical. Coupling the ionospheric models with thermospheric and magnetospheric models will lead to self-consistency and probably a predictive capability. Coupling to thermospheric models is currently under way; however, coupling with the magnetosphere must await the development of a magnetospheric model.