Black holes in four-dimensional General Relativity (GR) are remarkably constrained objects. Under suitable assumptions, stationary and isolated black holes are characterised by only a few macroscopic parameters, as established by the celebrated uniqueness and no-hair results. Their response to perturbations is governed by a spectrum of quasinormal modes (QNMs), whose frequencies and damping times encode information about the underlying spacetime and gravitational dynamics, providing a means of probing fundamental black hole properties and testing gravity. The growing availability of gravitational-wave data, together with the projected sensitivities of future observatories such as LISA and the Einstein Telescope, promises increasingly precise tests of GR and improved prospects for identifying new physics. This raises the questions: which black hole properties are robust, which change beyond GR, and which can be probed observationally? The aim of this internship is to explore black hole solutions and their QNMs, within GR and its extensions, focusing on the fundamental properties revealed by their perturbation spectra. Within GR, QNMs can probe questions on black hole structure and causality. Beyond GR, additional fields, modified gravitational interactions, or extra dimensions may alter black hole properties and perturbation spectra.