The deep atmospheres of giant planets exhibit dynamical phenomena that are at once familiar (e.g., alternating retrograde and prograde jets) and strange (e.g., winds do not dissipate at a solid surface). I will discuss general principles that govern the dynamics of such atmospheres, from how jets form in the upper atmospheres to how they are linked to the interior flow at depth. The energy and angular momentum balances constrain the flows that are possible. In the case of the giant planets of our solar system (Jupiter, Saturn, Uranus, and Neptune), these fundamental balances combined with observations of the upper atmospheres tightly constrain the flow and temperature structures that are possible in the interiors of the planets. I will discuss implications of these constraints for measurements by NASA's Juno mission (currently en route to Jupiter) and for exoplanets.