Because of composite materials’ excellent mechanical properties, they are widely used in aircraft manufacturing. Due to the large manufacturing deviation, there may be large gaps or interferences in the assembly of composite components. In addition, the brittleness of composite materials is large, and forced assembly may cause local damage between layers. Therefore, compared with metal materials, the assembly process of composites is more complex and the assembly demands are higher. Assembly gaps can be eliminated by measurement and compensation process, but the mechanical properties of shims are different from those of composite materials, and the gap compensation process lacks a unified standard, which may affect the assembly and service properties of composite components. This paper describes and summarizes the worldwide research progress about composites assembly, providing reference for future composites assembly.