Two-dimensional (2D) materials exhibit novel physical properties such as large exciton binding energy and the ability to be assembled as heterostructures. With the continuous development of 2D materials, their devices have shown significant potential in fileds such as optoelectronics, quantum information, and nanotechnology. Micro/nano-photonic cavities enable control of light-matter interactions at micro/nano-scale dimensions, offering an ideal platform for studying the exciton-photon coupling in the quantum regime. Consequently, the integration of 2D materials with micro/nano-photonic cavities has garnered considerable interest. This review summarizes representative devices that facilitate coupling between 2D materials and micro/nano-photonic cavities, with a focus on quasiparticle interactions and control in multiple degrees of freedom. By designing and manipulating these coupled systems, researchers can explore novel quantum phenomena such as exciton-photon polaritons and exciton-nanocavity coupling in the phononic degrees of freedom. The rich quantum effects observed in such systems demonstrate their notable potential for applications in quantum sources, nonlinear optics, and topological photonics. Despite challenges related to preparation and integration processes, and theoretical complexities involving strong correlations and many-body effects, the rapid progress in 2D material-micro/nano-photonic cavity coupling systems is opening new avenues for advancing quantum photonic technologies.