  We consider zero-temperature, stochastic Ising models with nearest-neighbor
interactions and an initial spin configuration chosen from a symmetric
Bernoulli distribution (corresponding physically to a deep quench). Whether a
final state exists, i.e., whether each spin flips only finitely many times as
time goes to infinity (for almost every initial spin configuration and
realization of the dynamics), or if not, whether every spin - or only a
fraction strictly less than one - flips infinitely often, depends on the nature
of the couplings, the dimension, and the lattice type. We review results,
examine open questions, and discuss related topics.
