  The vacuum correlations of the gravitational field are highly non-trivial to
be defined and computed, as soon as their arguments and indices do not belong
to a background but become dynamical quantities. Their knowledge is essential
however in order to understand some physical properties of quantum gravity,
like virtual excitations and the possibility of a continuum limit for lattice
theory. In this review the most recent perturbative and non-perturbative
advances in this field are presented. (To appear on Riv. Nuovo Cim.)
