The matter within a few Schwarzschild radii of accreting neutron stars and black holes is moving under the influence of a strong gravitational field, and, in stellar mass compact objects, through strongly curved spacetime. The X-rays emitted in the accretion process can be used to diagnose this motion, using both spectroscopy and rapid time variability. Similarly, X-rays emitted from the surface of accreting neutron stars can be used to diagnose neutron star mass, radius and even internal structure. I discuss these ways to probe strong gravitational fields and ultradense matter from an empirical perspective and in the context of proposed future X-ray observatories, in particular, LOFT.