This review provides an overview of cavity optomechanics, which explores the interaction between electromagnetic radiation and nano- or micromechanical motion. It covers the basics of optical cavities and mechanical resonators, their mutual optomechanical interaction mediated by the radiation pressure force, various experimental systems, optical measurements of mechanical motion, dynamical backaction amplification and cooling, nonlinear dynamics, multimode optomechanics, and future prospects for quantum optomechanics experiments. The review also discusses the fundamental implications for quantum physics and potential applications of optomechanical devices. Key topics include the principles of optomechanical coupling, Hamiltonian formulation, optomechanical equations of motion, experimental realizations, optomechanical parameters, static and dynamic phenomena, quantum optical measurements, cooling mechanisms, classical nonlinear dynamics, multimode setups, and quantum optomechanics. The review highlights the rapid advancements in the field, including the development of high-quality optical cavities and the exploration of novel mechanical elements, and emphasizes the potential for applications in quantum information processing and fundamental tests of quantum mechanics.This review provides an overview of cavity optomechanics, which explores the interaction between electromagnetic radiation and nano- or micromechanical motion. It covers the basics of optical cavities and mechanical resonators, their mutual optomechanical interaction mediated by the radiation pressure force, various experimental systems, optical measurements of mechanical motion, dynamical backaction amplification and cooling, nonlinear dynamics, multimode optomechanics, and future prospects for quantum optomechanics experiments. The review also discusses the fundamental implications for quantum physics and potential applications of optomechanical devices. Key topics include the principles of optomechanical coupling, Hamiltonian formulation, optomechanical equations of motion, experimental realizations, optomechanical parameters, static and dynamic phenomena, quantum optical measurements, cooling mechanisms, classical nonlinear dynamics, multimode setups, and quantum optomechanics. The review highlights the rapid advancements in the field, including the development of high-quality optical cavities and the exploration of novel mechanical elements, and emphasizes the potential for applications in quantum information processing and fundamental tests of quantum mechanics.