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 different approximation techniques. Many applications in gravitational physics, e.g. the detection of gravitational waves, crucially depend on our theoretical understanding and mastery of such approximation techniques.
In this talk we provide a brief review of the so-called 'problem of motion' in General Relativity. In particular we focus on multipolar approximation methods and their use in the description of the motion of extended test bodies.