Dynamical simulations have been developed at IASB-BIRA to model the deformations of the plasmasphere during geomagnetic substorms and other variations in the level of geomagnetic activity. The simulations are based on the mechanism of plasma instability and use the empirical Kp-dependent electric field E5D. The results of the simulations are compared with IMAGE observations that provide the first global comprehensive images of the Earth's plasmasphere. The predicted plasmapause positions correspond generally rather satisfactorily with the EUV observations. The plasmasphere is rather extended in all MLT sectors during quiet periods. During or just after geomagnetic substorms, the plasmaspause is sharper and becomes closer to the Earth in the night sector. Periods of enhanced geomagnetic activity are associated to the formation of plumes that rotate with the plasmasphere. The simulations reproduce the formation and the motion of these plumes, as well as the development of other structures like shoulders observed at the plasmapause by EUV on IMAGE.