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 governing equations for computer-controlled braiding in a table. A tabulation of applications of braided fabrics and composites is also provided. The article discusses the formation, structure, and properties, such as damage tolerance and impact damage limitation, of two-dimensional braid composites and three-dimensional braid composites.