This tutorial presents a brief introduction to the physical principles of cavity optomechanics. When light and mechanical motion are both confined in nanoscale structures, they can effectively couple through radiation pressure. This lecture discusses the quantum limits to optical measurement of mechanical motion and the basic physics of optomechanical interactions between photons and phonons. It reviews several recent developments in the field that exploit state transfer, breaking of time-reversal symmetry, and nonlinearities to develop new ways to control both light and motion in the classical and quantum domains.