In recent years, ternary layered carbide/nitride MAX phases and their derived two-dimensional nanolaminates MXenes have attracted extensive attention. The crystal structure of MAX phase is composed of M_n+1X_n unit interleaved with layers of A element. MAX phases combine good properties of metal and ceramic, which makes them promising candidates for high temperature structural materials, friction and wear devices, nuclear structural materials, etc. When etching the A-layer atoms of the MAX phase, the two-dimensional nanolaminates with the composition of M_n+1X_nT_x (T_x is surface termination), i.e. MXene, is obtained. MXenes have wide range of composition, and tunable physical and chemical properties, which endow them great potential in the applications of energy storage devices, electromagnetic shielding materials, and electronic devices, etc. In this paper, the research progress of MAX phase and MXene was introduced in terms of composition and structure, synthesis methods, and properties and application. Furthermore, the research prospects of this large family of materials were discussed.