This paper reviews the mainstream methods and recent advances in the nonlinear reduced order model (NLROM), with a particular focus on their applications in thin-walled structures. NLROM has emerged as an effective approach to overcome the computational inefficiency of traditional analysis methods, demonstrating significant potential for applications in dynamic strength design of thin-walled aerospace structures. First, this paper reviews the development history of NLROM, introduces the latest advancements in various methods, and summarizes typical workflow and commonly used approaches of many NLROMs. Specifically, the derivation and formulation of the NLROM governing equations are elaborated. Next, in terms of the construction and selection of the reduced function basis, five methods are discussed: linear normal modes, condensation of membrane effects, dual modes, modal derivatives, and proper orthogonal decomposition. For the calculation of nonlinear stiffness coefficients, the applied force method and the enforced displacement method are introduced. The advantages and limitations of various methods are analyzed and compared, with the superior performance of modal derivatives and the enhanced enforced displacement method being demonstrated in terms of analysis accuracy and computational efficiency. Finally, future research directions for NLROM are proposed.