Einstein’s general relativity is 100 years old. The theory has passed all experimental verifications with flying colors, but cosmological observations and difficulties in quantizing gravity suggest that general relativity should be modified at some level. Strong-field modifications of general relativity (if they occur in nature) will in general affect the dynamics of black holes and neutron stars with potentially observable signatures. Therefore compact objects – whether in isolation or in binary systems – are excellent astrophysical laboratories for high-energy physics and strong-field gravity. Furthermore, the gravitational radiation emitted during the inspiral and merger of compact binaries encodes important information on their astrophysical formation mechanism. I will discuss potential smoking guns of modified gravity in gravitational-wave detectors, and the theoretical and observational challenges associated with their search. I will also discuss the potential of Earth- and space-based detectors to further our understanding of the formation and evolution of compact binaries.