The field of engineering management usually involves evaluation issues,such as program selection,team performance evaluation,technology selection,and supplier evaluation.The traditional self-evaluation data envelop-ment analysis(DEA)method usually exaggerates the effects of several inputs or outputs of the evaluated decision-making unit(DMU),resulting in unrealistic results.To address this problem,scholars have proposed the cross-efficiency evaluation(CREE)method.Compared with the DEA method,CREE can rank DMUs more completely by using reasonable weights.With the extensive application of this technique,several problems,such as non-unique weights and non-Pareto optimal results,have arisen in CREE methods.Therefore,the improvement of CREE has attracted the attention of many scholars.This paper reviews the theory and applications of CREE,including the non-uniqueness problem,the aggre-gation of cross-efficiency data,and applications in engineering management.It also discusses the directions for future research on CREE.