The propagation of probe fields around black hole geometries is an interesting tool for the investigation of two important aspects: the stability of these geometry and the quasinormal modes spectra. In general, for simple enough metrics (e. g. spherically symmetric), the field equation reduces to a wave-like form with a specific potential. This turns the problem of integration into a wave scattering problem with a potential barrier similar to that of a Schrödinger equation in quantum mechanics. With the proper boundary conditions the spectrum is that of damped waves, the quasinormal modes. These represents the characteristic response of black holes in general to linear perturbations and give information about the stability of the geometry. In this talk I will refer some examples of quasinormal modes and destabilization of geometries in black holes in which a non-minimally coupled scalar field act, in the context of Horndeski theory. By using the same tools of field propagation, I still present some of our previous results in relation to the violation of strong cosmic censorship in charged geometries.