  In this contribution, we discuss the asymptotic safety scenario for quantum
gravity by evaluating the correlation functions of dynamical metric
fluctuations. This is done with a functional renormalisation group approach
that disentangles dynamical metric fluctuations from the background metric. We
detail the derivation of the respective flow equations on space-time manifolds
with Euclidean and Lorentzian signatures and discuss the diffeomorphism
symmetry constraints on the flow as well as the convergence of systematic
vertex expansion schemes. We then proceed with a comprehensive review of
results of momentum-dependent correlation functions at vanishing cutoff scale,
the phase structure of the asymptotically safe Standard Model, and spectral
properties of asymptotically safe gravity from direct computations in
space-times with Lorentzian signatures such as the graviton spectral function.
