Cavity optomechanical systems provide powerful platforms to manipulate photons and phonons,open potential applications for mode optical communications and precise measurements.With the refrigeration and ground-state cooling technologies,studies of cavity optomechanics are making significant progress towards the quantum regime including non-classical state preparation,quantum state tomography,quantum information processing,and future quantum inteet.With further research,it is found that abundant physical phenomena and important applications in both classical and quantum regimes appeal as they have a strong optomechanical nonlinearity,which essentially depends on the single-photon optomechanical coupling strength.Thus,engineering the optomechanical interactions and improving the single-photon optomechanical coupling strength become very important subjects.In this article,we first review several mechanisms,theoretically proposed for enhancing optomechanical coupling.Then,we review the experimental progresses on enhancing optomechanical coupling by optimizing its structure and fabrication process.Finally,we review how to use novel structures and materials to enhance the optomechanical coupling strength.The manipulations of the photons and phonons at the level of strong optomechanical coupling are also summarized.