  We investigate the emergence of a myriad of phases in the strong coupling
regime of the dipolar Hubbard model in two dimensions. By using a combination
of numerically unbiased methods in finite systems with analytical perturbative
arguments, we show the versatility that trapped dipolar atoms possess in
displaying a wide variety of many-body phases, which can be tuned simply by
changing the collective orientation of the atomic dipoles. We further
investigate the stability of these phases to thermal fluctuations in the strong
coupling regime, highlighting that they can be accessed with current techniques
employed in cold atoms experiments on optical lattices. Interestingly, both
quantum and thermal phase transitions are signalled by peaks or discontinuities
in local moment-local moment correlations, which have been recently measured in
some of these experiments, so that they can be used as probes for the onset of
different phases.
