Dimitrios Psaltis 2008-07-01 2008-11-18 Abstract Neutron stars and black holes are the astrophysical systems with the strongest gravitational fields in the universe. In this article, I review the prospect of using observations of such compact objects to probe some of the most intriguing general relativistic predictions in the strong-field regime: the absence of stable circular orbits near a compact object and the presence of event horizons around black-hole singularities. I discuss the need for a theoretical framework, within which future experiments will provide detailed, quantitative tests of gravity theories. Finally, I summarize the constraints imposed by current observations of neutron stars on potential deviations from general relativity. http://www.livingreviews.org/lrr-2008-9 Max Planck Institute for Gravitational Physics Neutron stars, Black holes, Tests of relativistic gravity Probes and Tests of Strong-Field Gravity with Observations in the Electromagnetic Spectrum