**Abstract: **Over the past years, electromagnetic and gravitational observations have been used to understand the nature of compact objects and the matter around them. However, our ability to learn about the underlying fundamental physics depends heavily on our understanding of the theory of gravity that describes the geometry around these compact objects, and the complex astrophysics that produces the observed radiation. If nature deviates from general relativity in the strong gravity regime, would we be able to measure possible observational signatures imprinted in the electromagnetic and gravitational spectra?

In this talk, I will discuss our current ability to constraint spacetimes that deviate parametrically from general relativity's classical solutions, using the electromagnetic radiation emitted by an accretion disk around a black hole, and the gravitational waves produced when comparable-mass black holes collide. I will finish by describing how combined measurements from NICER with LIGO/Virgo observations can perform a theory-agnostic and equation-of-state insensitive test of general relativity using neutron stars.