Black holes comprise a remarkably elegant set of solutions of the Einstein field equations. Aside from their rich mathematical structure, they are nowadays accepted as legitimate astrophysical objects and are routinely used in order to explain astrophysical observations. Nonetheless, General Relativity black holes were for a long time regarded with skepticism by many, even Einstein himself, as they imply infinite curvatures at their core (singularities) as well as infinite redshift at the horizon. What if nature tames somehow such infinities? How could we distinguish such “regularised black holes” from the standard ones? In this talk I shall try to present an overview of possibilities and their possible phenomenology with a specific attention at what could be observationally done in the near and far future.