  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...
