The inspiral of compact objects like black holes or neutron stars can
be approximated using point masses very well. However, very interesting
astronomical information is contained in effects to gravitational waves
arising from the object's higher multipoles (or their finite size).
Some of these effects can be modeled by an extension of the point mass
action. Based on such an action, contributions of dipole (i.e., spin)
and quadrupole to the post-Newtonian (PN) approximation can be
obtained. The quadrupole effects are the first which encode information
of the internal structure of the compact objects, e.g., they allow an
distinction between black holes and neutron stars and also different
equations of state.