The complex geometry of rotating machines makes the flows strongly affected by rotation and curvature, which are challenging for turbulence modeling. During the development of CFD, large amount of turbulence models appeared and hence make the user hard to decide which one to choose. The present paper presents a coherent review of the various approaches proposed in the recent literatures on this topic. First, the influence of the rotation and curvature is reviewed and concluded. Then, the basic concepts of RANS and LES are introduced to facilitate the description of the models and each method is classified into several types. A variety of models are then described and assessed either by the results in the literatures or by own results, with special concentration on the application to rotating machines. Finally, a brief introduction to the hybrid RANS/LES is made and assessed, together with the recommendation for the selection of the models. The aim of the review is to provide information on the advantages and limitations of related models and make it easier for the user to choose an appropriate model.