Heteronuclear polar molecules prepared in the electronic and vibrational ground
state and cold gases of Rydberg-excited alkali atoms provide examples of systems
where long-range dipole-dipole interactions can dominate the system dynamics.
In this talk we present recent theoretical results on the possibility of
realizing quantum phases of matter with strong long-range interactions in the
cold atom/molecule context, with a focus on dipole-dipole interactions. These
phases include supersolid phases in the mesoscopic and thermodynamic regimes,
as well as crystalline phases of cold Rydberg atoms and polar molecules.