This paper describes results of data-based modeling of the magnetospheric configuration and its response to changes in the solar wind dynamical pressure and the IMF. Previous models did not have a pre-defined magnetopause, they were calibrated by the Kp-index only, and thus did not allow proper modeling of solar wind effects. The new models explicitly include (i) the solar-wind-controlled magnetopause, (ii) Region 1 and 2 Birkeland currents, and (iii) the interconnection of the magnetospheric and solar wind fields at the boundary. They predict the most significant effects of solar wind variations upon the global magnetospheric structure. On the dayside, the Region 1 Birkeland currents cause major changes of the magnetic configuration, as the IMF turns southward. The tail current intensity is controlled mainly by the pressure of the solar wind, although the influence of the southward IMF is also clearly seen. The effects of the IMF-induced interconnection field were found to be quite significant.