  Black hole quasinormal frequencies are complex numbers that encode
information on how a black hole relaxes after it has been perturbed and depend
on the features of the geometry and on the type of perturbations. On the one
hand, the examples studied so far in the literature focused on the case of
black hole geometries with singularities in their interior. On the other hand,
it is expected that quantum or classical modifications of general relativity
may correct the pathological singular behavior of classical black hole
solutions. Despite the fact that we do not have at hand a complete theory of
quantum gravity, regular black hole solutions can be constructed by coupling
gravity to an external form of matter, sometimes modeled by one form or another
of nonlinear electrodynamics. It is therefore relevant to compute quasinormal
frequencies for these regular solutions and see how differently, from the
ordinary ones, regular black holes ring. In this paper, we take a step in this
direction and, by computing the quasinormal frequencies, study the quasinormal
modes of neutral and charged scalar field perturbations on regular black hole
backgrounds in a variety of models.
