Natural geodynamic processes in the Earth crust become apparent as different types of movement. These movements can be regular when different strata move along fault lines on a local scale or along boundaries of tectonic plates on a continental scale. They can also be abrupt and have the form of earthquakes and other major seismic events. Both forms of movement are irreversible, and thus they can be called deformations. Analysis of Earth crust motion and deformations can be performed by means of seismic soundings, strain-meter and tilt-meter readings, and geodetic methods which are the most significant ones. Geodesy plays a key role in crustal deformation studies by determining the temporal variations of the Earth shape and size at various spatial and time scales. Among modern geodetic methods space geodesy applications are of most importance. Among the latter Global Positioning Systems NAVSTAR-GPS and GLONASS should be pointed out. Current research corresponds an overview of certain GPS applications for Earth crust motion and deformation analysis and geodynamical and geophysical solutions.