What is observable in classical and quantum gravity?

The problem of the identification of the observable quantities in quantum gravity (or in any diffeomorphism invariant quantum theory) is considered. The author recalls Einstein's 'hole argument' on the impossibility of a priori identifying spacetime points. He argues that only by explicitly taking into account the physical nature of the bodies that form the reference system and their gravitational interactions one can get well defined gauge-invariant (and 'local') observables and a definition of physical spacetime points. A model is considered in which general relativity is coupled to matter: the matter represents the physical reference system. The gauge-invariant physical observables of this theory are displayed.