We describe recent progress in physics-based models of the plasmasphere using the fluid and the kinetic approaches. Global modeling of the dynamics and influence of the plasmasphere is presented. Results from global plasmasphere simulations are used to understand and quantify (i) the electric potential pattern and evolution during geomagnetic storms, and (ii) the influence of the plasmasphere on the excitation of electromagnetic ion cyclotron (EMIC) waves and precipitation of energetic ions in the inner magnetosphere. The interactions of the plasmasphere with the ionosphere and the other regions of the magnetosphere are pointed out. We show the results of simulations for the formation of the plasmapause and discuss the influence of plasmaspheric wind and of ultra low frequency (ULF) waves for transport of plasmaspheric material. Theoretical models used to describe the electric field and plasma distribution in the plasmasphere are presented. Model predictions are compared to recent CLUSTER and IMAGE observations, but also to results of earlier models and satellite observations. © 2009 Springer Science+Business Media B.V.