Abstract: In the reliability-based topology optimization, the uncertainty is considered during the engineering practice, which is important in a structural reliability design. At present, the most commonly used reliabilitybased topology optimization methods for a continuum structure are: the nested optimization method, the decoupling method, the single-loop method and the reliability safety coefficient method. Firstly, the mathematical models of the reliability-based topology optimization are introduced. Then, the theoretical basis of above methods are systematically discussed, and their current researches and applications are briefly reviewed. Finally, the advantages, disadvantages and development trends of above methods are discussed.