The book "Equations of Motion in Relativistic Gravity" offers a comprehensive examination of the derivation of the equations of motion in both general relativity and alternative theories of gravity. It covers a wide range of topics, from the description of test bodies to self-gravitating bodies, incorporating both current and future observations. Special attention is given to the various approximation methods that are widely used in the context of the relativistic motion problem. The applications discussed in this work include the motion of binary systems and the gravitational waves emitted by these systems, as well as observations of the galactic center. The book emphasizes how fundamental theoretical choices can influence the interpretation of experiments. It provides a current status report that is valuable for both professionals and students with a background in general relativity.