The design of a space transportation system is a complex multidisciplinary optimization problem. Uncertainty existing at the early phases of the design process influences the final system performances and reliability. Uncertainty-based Multidisciplinary Design Optimization (UMDO) methodologies allow to determine the optimal design solution with respect to the performance criteria while ensuring the reliability and the robustness of the final system to uncertainty. They enable to handle the disciplinary couplings and to facilitate the search of compromises between conflicting objectives. This paper provides a survey of the UMDO process. Different techniques such as uncertainty modeling, uncertainty propagation or optimization problem formulation are presented and a qualitative comparison of the UMDO methodologies is performed in order to provide general guidelines. A literature review of case studies of UMDO process applied to aerospace systems is provided. Moreover, open issues that need to be addressed in order to develop an efficient UMDO framework for the design of space transportation systems are discussed and future trends for UMDO are highlighted.