Compact astrophysical objects, like black holes and neutron stars, are opening a new and enlightening window on gravity. The study of such objects in strong curvature regimes now allows us to test alternative gravity theories, and notably the existence of other fundamental fields. I will discuss no-hair theorems, and how one can still build solutions that deviate from general relativity. I will investigate some exact black hole solutions and numerical neutron star solutions, together with the associated observational imprints. I will also establish a universal result for the geodesics of such compact objects, showing that test bodies always fall towards minima of the generalized Newtonian potential.
