In this thesis, I study the ways in which modified theories of gravity might be tested for using black holes. In particular, I focus on ways in which the gravitational waves emitted during the 'ringdown' of a perturbed black hole may be affected. I will develop and demonstrate the use of a framework for analysing the evolution of perturbations in arbitrary modified gravity theories in both cosmological and black hole backgrounds. I will use this to show that the characteristic Quasi-normal mode (QNM) spectrum of frequencies for the gravitational waves emitted from a perturbed black hole may be altered even in the case that the background black hole is identical to a general relativistic black hole. This is purely due to the presence, and coupling to, additional gravitational degrees of freedom. I will also explore the landscape of hairy black hole solutions in the wake of the multi- messenger observation of GW/GRB170817, and show that it is increasingly difficult to endow a black hole with scalar hair in modified gravity given the constraint that gravita- tional waves must propagate at the speed of light. In addition, black hole perturbations in General Relativity are analysed, with analytic expressions for QNM frequencies calculated for scalar, vector, and gravitational perturba- tions to a slowly rotating Kerr-(Anti-)de Sitter black hole. Finally, I will examine the specific case of black hole perturbations in Horndeski the- ory, demonstrating the qualitative difference in gravitational wave emission from a per- turbed black hole in General Relativity and in Horndeski gravity. I will also forecast the detectability of such a modified gravitational wave signal, and estimate what constraints one might be able to place on fundamental parameters of Horndeski gravity through gravi- tational wave observations.