Over 3700 planets have been discovered around other stars, many of which orbit extremely close-in, where they receive enormous stellar fluxes. The intense radiation on these planets is expected to drive a vigorous atmospheric circulation that shapes the day-night temperature difference, infrared light curves, spectra, albedo, atmospheric composition, and perhaps even the long-term evolution and planetary radii. Recent space-based and ground-based telescope observations exhibit extensive evidence for such circulations in the atmospheres of these planets. This new observational vanguard opens the possibility of extending our understanding of atmospheric circulation beyond the confines of the Solar System, and it raises fundamental questions about planetary climate and habitability. Here I will survey this exciting new field and describe recent research elucidating the dynamical mechanisms that operate to control the atmospheric circulation in these planets' atmospheres. To emphasize the similarities as well as differences, I will ground this discussion in our understanding of the more familiar atmospheric dynamical regime of Earth, as well as our "local" giant planets Jupiter, Saturn, Uranus, and Neptune.