Abstract Braided structures are unique in their high level of conformability, torsional stability, and damage resistance. This article describes the classifications of braiding such as two-dimensional braiding and three-dimensional braiding. It presents the governing equations for computer-controlled braiding in a table. The article lists the applications of braided fabrics and composites. It discusses the formation, structure, and properties of two-dimensional braid composites and three-dimensional braid composites: the damage tolerance and the impact damage limitation.