A systematic multi-disciplinary design approach to the optimum tailoring of composite materials is a challenging design optimization problem. It involves the tailoring of composite material properties as per the design requirements. While designing any component, typical cost or weight reduction involves the use of optimization together with corresponding analysis. Depending upon various performance requirements, different types of analyses become the design drivers. Often in practice, such design drivers are dealt with separately, allowing the design to iterate until all the constraints are satisfied. However, these all-design drivers act as separate black box units with very tight interfaces, which could lead to quite inefficient designs. Multidisciplinary Design Optimization (MDO) establishes a link between numerous parameters concerning various disciplines. The main objective of this study is to review the different MDO frameworks applied to the design optimization of composite materials and structures by various researchers and to compare their capabilities and constraints. © 2021 Elsevier Ltd