Measurements of black-hole spins are of crucial importance to fulfill the promise of gravitational-wave astronomy. On the astrophysics side, spins are perhaps the cleanest indicator of black-hole evolutionary processes, thus providing a preferred way to discriminate how LIGO's black holes form. On the relativity side, spins are responsible for peculiar dynamical phenomena (from precessional modulations in the long inspiral to gravitational-wave recoils at merger) which encode precious information on the underlying astrophysical processes. I present some examples to explore this deep and fascinating interplay between spin dynamics (relativity) and environmental effects (astrophysics). Black-hole spins indeed hide remarkable surprises on both fronts: morphologies, resonances, constraints on supernova kicks, multiple merger generations and more... These findings were presented at 12th Edoardo Amaldi Conference on Gravitational Waves, held on July 9-14, 2017 in Pasadena, CA, USA.