  We review the quantum theory of cooling of a mechanical oscillator subject to
the radiation pressure force due to light circulating inside a driven optical
cavity. Such optomechanical setups have been used recently in a series of
experiments by various groups to cool mechanical oscillators (such as
cantilevers) by factors reaching $10^{5}$, and they may soon go to the ground
state of mechanical motion. We emphasize the importance of the
sideband-resolved regime for ground state cooling, where the cavity ring-down
rate is smaller than the mechanical frequency. Moreover, we illustrate the
strong coupling regime, where the cooling rate exceeds the cavity ring-down
rate and where the driven cavity resonance and the mechanical oscillation
hybridize.
