A database is compiled for the study of solar and heliospheric causes of geomagnetic perturbations with the daily average index Ap > 20 that were observed in the period 1997 2000. The number of such events (more than 200) progressively increased and fluctuated as the current solar cycle developed. It is established that geomagnetic storms are generated by dynamical processes and structures near the center of the solar disk in a zone of several tens of degrees, and these processes are responsible for the appearance in the Earth's region, within several tens of hours, of quasistationary and transient solar wind streams with a sufficiently strong southward component of the heliospheric magnetic field. These streams lasted more than a few hours. The following structures can serve as morphological indicators for the prediction of the appearance of such streams: (1) active and disappearing filaments derived from synoptic H-maps of the Sun, (2) solar flares, (3) coronal holes and evolving active regions, and (4) the heliospheric current sheet. The geometry of coronal mass ejections needs further observational study.