  The motion of a compact body in space and time is commonly described by the
world line of a point representing the instantaneous position of the body. In
General Relativity such a world-line formalism is not quite straightforward
because of the strict impossibility to accommodate point masses and rigid
bodies. In many situations of practical interest it can still be made to work
using an effective hamiltonian or energy-momentum tensor for a finite number of
collective degrees of freedom of the compact object. Even so exact solutions of
the equations of motion are often not available. In such cases families of
world lines of compact bodies in curved space-times can be constructed by a
perturbative procedure based on generalized geodesic deviation equations.
Examples for simple test masses and for spinning test bodies are presented.
