  The literature on quantum-gravity-inspired scenarios for the quantization of
spacetime has so far focused on particle-physics-like studies. This is partly
justified by the present limitations of our understanding of quantum-gravity
theories, but we here argue that valuable insight can be gained through
semi-heuristic analyses of the implications for gravitational phenomena of some
results obtained in the quantum-spacetime literature. In particular, we show
that the types of description of particle propagation that emerged in certain
quantum-spacetime frameworks have striking implications for gravitational
collapse and for the behaviour of gravity at large distances.
