Geodynamics is the application of the basic principles of physics, chemistry and mathematics to understanding how the internal activity of the Earth results in all the geological phenomena and structures apparent at the surface, including seafloor speading and continental drift, mountain building, volcanoes, earthquakes, sedimentary basins, faulting, folding, and more. Geodynamics also deals with how the Earth's internal activity and structure reveals itself externally in ways both geophysical, its gravitational and magnetic fields, and geochemical, the mineralogy of its rocks and the isotopic composition of its rocks, atmosphere, and ocean. The discipline of geodynamics did not exist until about the early 1970s. The plate tectonics revolution was the impetus for the birth of the subject. Today, geodynamics goes beyond the Earth to consider the interiors and surfaces of other planets and moons in our solar system. While this aspect of the science could be termed planetary dynamics, it involves the same geodynamical processes that shape the Earth, though often with intriguingly different outcomes for the other bodies. Mathematical modeling, which attempts to understand a phenomenon quantitatively, lies at the heart of geodynamics. In the early years of the subject analytic and semi-analytic methods were sufficient to gain insights into the workings of the Earth's interior. After four decades of progress in the subject it is, generally speaking, no longer possible to address the remaining questions with such simple models.