The occurrence of turbulent pulsations in straight pipes of noncircular cross-section leads to the situation, when the average velocity field includes not only the longitudinal component but also transverse components that form a secondary flow. This hydrodynamic phenomenon discovered at the twenties of the last century (J. Nikuradse, L. Prandtl) has been the object of active research to the present day. The intensity of the turbulent secondary flows is not high; usually, it is not greater than 2–3% of the characteristic flow velocity. Nevertheless, their contribution to the processes of transverse transfer of momentum and heat is comparable to that of turbulent pulsations. In this paper, a review of experimental, theoretical, and numerical studies of secondary flows in straight pipes and channels is given. Emphasis is placed on the issues of revealing the physical mechanisms of secondary flow formation and developing the models of the apriori assessment of their forms. The specific features of the secondary flow development in open channels and channels with inhomogeneously rough walls are touched upon. The approaches of semiempirical simulation of turbulent flows in the presence of secondary flows are discussed.