  We review the present status of quantum-gravity phenomenology in relation to
gravitational waves (GWs). The topic can be approached from two direction, a
model-dependent one and a model-independent one. In the first case, we
introduce some among the most prominent cosmological models embedded in
theories of quantum gravity, while in the second case we point out certain
common features one finds in quantum gravity. Three cosmological GW observables
can be affected by perturbative as well as non-perturbative quantum-gravity
effects: the stochastic GW background, the propagation speed of GWs and the
luminosity distance of GW sources. While many quantum-gravity models do not
give rise to any observable signal, some predict a blue-tilted stochastic
background or a modified luminosity distance, both detectable by future GW
interferometers. We conclude that it is difficult, but still possible, to test
quantum gravity with GW observations.
