  Systems of strongly interacting dipoles offer an attractive platform to study
many-body localized phases, owing to their long coherence times and strong
interactions. We explore conditions under which such localized phases persist
in the presence of power-law interactions and supplement our analytic treatment
with numerical evidence of localized states in one dimension. We propose and
analyze several experimental systems that can be used to observe and probe such
states, including ultracold polar molecules and solid-state magnetic spin
impurities.
