Brown dwarfs and relatively isolated young extrasolar giant planets occupy an important parameter space to understand planetary atmospheres. Recent observations of these worlds have provided unprecedented details to probe atmospheric dynamics in a new regime, raising critical questions about mechanisms generating the global circulation and its fundamental nature. Two major mechanisms have been proposed. The first is a mechanically forced scenario in which interior convection interacts with the overlying stratified atmospheres and generates a wealth of waves and turbulence. These atmospheric eddies interact with the large-scale flows, driving global circulation. The second scenario is a thermally-driven mechanism linked to cloud radiative feedback. In this talk, I will introduce the principles of these mechanisms and highlight the properties of the resulting circulation patterns. I will show that vigorous atmospheric flows, including large-scale turbulence and vortices, waves, and zonal jets are typical outcomes. Lastly, connections and implications to observations will be discussed.