This talk aims at emphasising the key role played by the hyperboloidal scheme in casting (linear) scattering on black holes as a non-normal dynamics problem, in particular prompting its study under a non-modal analysis approach. Indeed, non-normal dynamics naturally brings into scene concepts and tools from the theory of non-selfadjoint operators and non-modal analysis. Such a shift in perspective offers a complementary view to the sound and well-developed theory of scattering and, most importantly, opens a path to the formulation of new questions specically addressing the presence of characteristic non-normal effects in spacetime dynamics.