  We study quasi-normal modes of black holes, with a focus on resonant (or
quasi-normal mode) expansions, in a geometric frame based on the use of
conformal compactifications together with hyperboloidal foliations of
spacetime. Specifically, this work extends the previous study of Schwarzschild
in this geometric approach to spherically symmetric asymptotically flat black
hole spacetimes, in particular Reissner-Nordstr\"om. The discussion involves,
first, the non-trivial technical developments needed to address the choice of
appropriate hyperboloidal slices in the extended setting as well as the
generalization of the algorithm determining the coefficients in the expansion
of the solution in terms of the quasi-normal modes. In a second stage, we
discuss how the adopted framework provides a geometric insight into the origin
of regularization factors needed in Leaver's Cauchy based foliations, as well
as into the discussion of quasi-normal modes in the extremal black hole limit.
