Understanding space weather and forecasting geomagnetic storms are the most important applications of solar-terrestrial physics. Geomagnetic storms are complex sequences of physical processes, which include both microprocesses, (e.g., magnetic reconnection) and macroprocesses (relaxation of the ring current around the Earth, which is the main contributor to the geomagnetic storms). To derive a mathematical description of the magnetospheric dynamics from first principles the models of all processes involved should be conjugated into a global model. This goal will ultimately be accomplished. However the present level of understanding means that this will not happen in the foreseeable future. An alternative approach used here is based on system identification. A physically interpretable continuous time model capturing the magnetospheric dynamics has been identified directly from measurements of the solar wind and geomagnetic Dst index. It is shown that such a model can provide reliable forecasts of geomagnetic disturbances.