Data assimilation models are widely used in meteorology, oceanography and space science for both science studies and practical applications. During the last decade, we have developed, and are continuing to develop, four physics-based data assimilation models of the ionosphere, thermosphere and electrodynamics. Two of the models pertain to the ionosphere and were developed under a program called Global Assimilation of Ionospheric Measurements (GAIM). The first is a Gauss-Markov Kalman Filter model (GAIM-GM) and it uses a physics-based model of the ionosphere and a Kalman filter as a basis for assimilating a diverse set of measurements. The physics-based model is the Ionosphere Forecast Model (IFM), which is global and covers the E-region, F-region, and topside from 90 to 1400 km. It takes account of five ion species (NO⁺, O₂⁺, N₂⁺, O⁺, H⁺), but the main output of the model is a 3-dimensional electron density distribution. The second data assimilation model uses a physics-based ionosphere-plasmasphere model and a ensemble Kalman filter as a basis for assimilating the measurements. This ‘full physics' model (GAIM-FP) is global, takes account of six ion species (NO⁺, O₂⁺, N₂⁺, O⁺, H⁺, He⁺), covers the altitude range of from 90 to 30,000 km, and is more sophisticated than the Gauss-Markov model. The GAIM models can assimilate bottom-side N_e profiles from hundreds of ionosondes, slant TEC from 1000 ground GPS/TEC receivers, in situ N_e from 4 DMSP satellites, occultation data from multiple satellites, and both limb and disk UV emissions measured by satellites. The third data assimilation model that we developed is a physics-based ensemble Kalman filter for high-latitude ionosphere dynamics and electrodynamics. This model assimilates cross-track ion velocities from the 4 DMSP satellites, line-of-sight ion velocities from the SuperDarn radar system, and magnetic perturbations from 100 ground magnetometers and from the Iridium constellation of satellites. We have also developed an ensemble Kalman filter model for the global thermosphere, but it is not as far along as the other three data assimilation models. The characteristics and uses of these models for science and applications will be discussed.