Title: "Motion of extended bodies in General Relativity"

The description of the motion of extended bodies represents a long-standing problem in the context of Einstein's theory of gravity. In general, the study of extended self-gravitating objects in General Relativity requires the use of approximation techniques. Many applications in gravitational physics, e.g. the detection of gravitational waves, crucially depend on our understanding and mastery of different approximation schemes. In this talk we provide a brief review of the so-called 'problem of motion' in General Relativity and related conceptual problems in the context of relativistic approximation schemes. In particular we focus on a multipolar method, which was recently used to derive the equations of motion for extended bodies up to the quadrupolar order and beyond.