The study of Black-Hole perturbation theory is a classical problem in General Relativity and crucial to study gravitational waves. Due to the high order of symmetry of the BH gravitational field and the consequent separation of variables, the first order problem reduces to the study of linear ordinary second order differential equations. The resulting ODEs are of Fuchsian type and therefore, as already observed long ago by A.M.Polyakov, can be solved exactly in terms of classical - regular or irregular - Virasoro conformal blocks. By making use of the specific explicit expressions of the latter implied by the AGT dual perspective (susy gauge theory) on the conformal field theory, it is possible to explicitly solve the connection problem of the resulting (confluent)Heun equation and give novel exact and explicit formulas for the grey body factor, quasi-normal modes and Love numbers of diverse black holes. This will be also explicitly applied to 4D Kerr and Schwarzschild-(A)de Sitter BHs. Moreover we will apply the above results to compute BH Compton scattering amplitudes and effective acions in the BHs background.