  Quantum manipulation of macroscopic mechanical systems is of great interest
in both fundamental physics and applications ranging from high-precision
metrology to quantum information processing. A crucial goal is to cool the
mechanical system to its quantum ground state. In this review, we focus on the
cavity optomechanical cooling, which exploits the cavity enhanced interaction
between optical field and mechanical motion to reduce the thermal noise. Recent
remarkable theoretical and experimental efforts in this field have taken a
major step forward in preparing the motional quantum ground state of mesoscopic
mechanical systems. This review first describes the quantum theory of cavity
optomechanical cooling, including quantum noise approach and covariance
approach; then the up-to-date experimental progresses are introduced. Finally,
new cooling approaches are discussed along the directions of cooling in the
strong coupling regime and cooling beyond the resolved sideband limit.
