Publications about the earthquake foci migration have been reviewed. An important result of such studies is establishment of wave nature of seismic activity migration that is manifested by two types of rotational waves; such waves are responsible for interaction between earthquakes foci and propagate with different velocities. Waves determining long-range interaction of earthquake foci are classified as Type 1; their limiting velocities range from 1 to 10 cm/s. Waves determining short-range interaction of foreshocks and aftershocks of individual earthquakes are classified as Type 2; their velocities range from 1 to 10 km/s. According to the classification described in [Bykov, 2005], these two types of migration waves correspond to slow and fast tectonic waves. The most complete data on earthquakes (for a period over 4.1 million of years) and volcanic eruptions (for 12 thousand years) of the planet are consolidated in a unified systematic format and analyzed by methods developed by the authors. For the Pacific margin, Alpine-Himalayan belt and the Mid-Atlantic Ridge, which are the three most active zones of the Earth, new patterns of spatial and temporal distribution of seismic and volcanic activity are revealed; they correspond to Type 1 of rotational waves. The wave nature of the migration of seismic and volcanic activity is confirmed. A new approach to solving problems of geodynamics is proposed with application of the data on migration of seismic and volcanic activity, which are consolidated in this study, in combination with data on velocities of movement of tectonic plate boundaries. This approach is based on the concept of integration of seismic, volcanic and tectonic processes that develop in the block geomedium and interact with each other through rotating waves with a symmetric stress tensor. The data obtained in this study give grounds to suggest that a geodynamic value, that is mechanically analogous to an impulse, remains constant in such interactions. It is thus shown that the process of wave migration of geodynamic activity should be described by models with strongly nonlinear equations of motion.