Cavity optomechanics studies the interaction between photons and macroscopic mechanical oscillators. Now it has become an important field for the study of the transition between the quantum world and the classicalworld, as well as the non-classical and nonlinear effects. This paper first introduces some basic physical concepts in this field, including radiation pressure, optomechanical Hamiltonian, Heisenberg-Langevin equation, and linearization of equations. Then we review some progress of the novel optomechanical effects in recent years, including optomechanically induced transparency, nonreciprocal light propagation, high-order sideband generation, and optomechanical entanglement. Finally, some research prospects are proposed.