Abstract: Simplifying an engineering design by removing geometric details before simulation can significantly reduce the complexity of downstream tasks of mesh generation and field solution computations, and improve the mesh quality and the computation reliability. However, the simplification process will inevitably change the underlying computational domain, and produce different engineering analysis results, resulting in defeaturing error. Due to the lack of theories on quantitative control of the errors induced by design simplification and associated implementation approaches, the simplification process is still mainly performed manually, very time-consuming, and remains a bottleneck issue in seamless CAD/CAE integration, and is urgently to be resolved. To help address this issue, this paper surveys related research efforts on the topic of engineering analysis reliable CAD model simplification, summarizing background and importance of the problem, an overall flowchart to resolve it, and recent research progress on resolving the important issue. This multi-discipline research topic is related to various researches on CAD, CAE, computational physics, PDE theories etc., while the survey mainly focuses on progresses on its two core issues: geometric operations to remove details or to generate the simplification model, and quantitative estimations of the impact of removing a single or a set of features to engineering analysis. Future directions on the topic are also discussed in the end.