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General relativity has been tested by many experiments, which, however,almost exclusively probe weak spacetime curvatures. In this thesis, I createtwo frameworks for testing general relativity in the strong-field regime withobservations of black holes in the electromagnetic spectrum using current ornear-future instruments. In the first part of this thesis, I design tests ofthe no-hair theorem, which uniquely characterizes the nature of black holes ingeneral relativity in terms of their masses and spins and which states thatthese compact objects are described by the Kerr metric. I investigate aquasi-Kerr metric and construct a Kerr-like spacetime, both of which contain anindependent parameter in addition to mass and spin. If the no-hair theorem iscorrect, then any deviation from the Kerr metric has to be zero. I show thatalready moderate changes of the deviation parameters in either metric lead tosignificant modifications of the observed signals. I apply this framework tothe imaging of supermassive black holes using very-long baseline interferometryas well as to the quasi-periodic variability and relativistically broadenediron lines observed in both galactic and supermassive black holes. In thesecond part of this thesis, I devise a method to test the predicted evaporationof black holes in Randall-Sundrum-type braneworld gravity through the orbitalevolution of black-hole X-ray binaries and obtain constraints on the size ofthe extra dimension from A0620-00 and XTE J1118+480.

Testing General Relativity in the Strong-Field Regime with Observations of Black Holes in the Electromagnetic Spectrum