At zero temperature, the natural Markov process of Ising spin configurations on Zd (or other lattices) is that each spin flips with rate 1 or 0 or 1/2 according to whether the flip would lower the energy or raise it or leave it unchanged. What happens as time t tends to infinity when the initial state is chosen by independent tosses of a fair coin? Do spins flip finitely or infinitely many times? Does the state after a large time depend more on the initial state or on the realization of the dynamics ("nature vs. nurture")? Do the answers to such questions depend on the dimension, on the lattice, on whether the Ising model is disordered?