Hydraulic forces occurring in rotodynamic pumps, especially those in power industry where they are essential in ensuring reliable pump performance, are important for appropriate sizing of shaft and bearings, proper designing the balancing device and avoiding the excessive pump vibration. Accuracy of the prediction of the forces is still not satisfactory. The reasons of and methods for predicting stable and unstable axial and radial thrust are comprehensively discussed. Three kinds of the pressure distribution assessment in the impeller sidewall gaps to get axial thrust are analyzed i.e. empirical, integral and RANS. Empirical and numerical investigations are presented. Additional issues important for predicting axial thrust are thoroughly analyzed such as impeller and balancing device annular seals flows, similarity laws for axial thrust, impeller internal force, forces in open and semi-open impellers. The issues of balancing axial thrust are also analyzed. The results of measurements and predictions of radial thrust in a single volute centrifugal pump are presented and methods of balancing discussed. The dynamic forces in annular seals are discussed. Unsteady interaction between impeller and diffuser and rotating stall are analyzed.