  It is congruous with the quantum nature of the world to view the space-time
geometry as an emergent structure that shows classical features only at some
observational level. One can thus conceive the space-time manifold as a purely
theoretical arena, where quantum states are defined, with the additional
freedom of changing coordinates like any other symmetry. Observables, including
positions and distances, should then be described by suitable operators acting
on such quantum states. In principle, the top-down (canonical) quantisation of
Einstein-Hilbert gravity falls right into this picture, but is notoriously very
involved. The complication stems from allowing all the classical canonical
variables that appear in the (presumably) fundamental action to become quantum
observables acting on the "superspace" of all metrics, regardless of whether
they play any role in the description of a specific physical system. On can
instead revisit the more humble "minisuperspace" approach and choose the
gravitational observables not simply by imposing some symmetry, but motivated
by their proven relevance in the (classical) description of a given system. In
particular, this review focuses on compact, spherically symmetric, quantum
mechanical sources, in order to determine the probability they are black holes
rather than regular particles. The gravitational radius is therefore lifted to
the status of a quantum mechanical operator acting on the "horizon
wave-function", the latter being determined by the quantum state of the source.
This formalism is then applied to several sources with a mass around the
fundamental scale, which are viewed as natural candidates of quantum black
holes.
