The secondary flow is the concomitant flow of the mainstream, which generally exists in nature and turbomachinery, most typically in the turbomachinery. The secondary flow in the turbomachinery not only changes the motion of the mainstream, deteriorates the flow field, induces the boundary layer separation, intensifies the jet wake at the exit, but also generates flow losses and noise. It is therefore of increasing concern of scholars and has risen to the same research level as the potential flow theory. Since 1950s, scholars at home and abroad have studied the phenomenon of the secondary flow from the perspectives of theoretical analysis, experimental research and numerical simulation, gradually understanding the flow mechanism and structure of the secondary flow in turbomachinery and establishing a continuously improving mathematical model, loss assessment and experimental methods for the secondary flow. Starting from the phenomenon of the secondary flow, the flow structure, mathematical model, and loss calculation and test methods of the secondary flow of the turbomachinery are reviewed and summarized. It is pointed out that the classical theoretical model of the secondary flow based on streamwise vortex built by ZANGENEH has some limitations. The key directions for future research are proposed based on the S3 flow surface theory of the secondary flow. It can provide references for the improvement of the flow field quality and the hydrodynamic performance of various types of turbomachinery, including waterjet pumps.