The linear prediction filters computed by Bargatze et al. [1985> have resulted in a turning point in the study of solar wind-magnetosphere coupling. The evolution of the filters with varying activity provides a clear demonstration that the coupling is nonlinear. The filters have thus brought about the end of one era of linear correlative studies and the beginning of a new era of nonlinear dynamical studies. Two separate, but complementary, approaches have emerged in these dynamical studies, analogue modeling and data-based phase space reconstruction. The reconstruction research has evolved from the original autonomous method studies, which were not conclusive, to the more recent input-output studies that are more appropriate for the solar wind-driven magnetosphere and have produced more reliable results. At present it appears that the modeling and reconstruction approaches may be merged in future attempts to produce analogue models directly from the results of the input-output data-based methods. If this can be accomplished, it will constitute a major step forward toward the goal of a low-dimensional analogue model of the magnetospheric dynamics derived directly from data and interpreted in terms of magnetospheric physics. These developments are reviewed in three sections: autonomous data analysis methods, analogue models, and input-output data analysis methods. The introduction provides sufficient information to read each of these sections independently. ¿ American Geophysical Union 1996