The main focus of the network is on the interplay between gravity and quantum mechanics. Over the last decade several studies provided evidence of the fact that some effects introduced genuinely at the Planck length might be studied experimentally. In most such scenarios the large distance scales involved in observations in astrophysics and cosmology play a role: minute Planck-length quantum-spacetime effects have a chance to cumulate to observably large level over such long propagation distances. We contribute to the further development of this phenomenology, but at the same time we deal with the theoretical challenges of deriving predictions from the rather complex formalizations of quantum spacetime that appear to be invited by the structure of the quantum-gravity problem. Our team has strong expertise on all fronts relevant for this ambitious research program, both for quantum-gravity-phenomenology research and for quantum-gravity theory research, particularly concerning two approaches that we shall use as primary guidance: the approach based on spacetime noncommutativity and the approach based on condensed-matter-analogue models of gravity.