This work firstly reviews the experimental data for centrifugal pumps operating in steady-state and transient two-phase flow. The pump head and torque become degraded in two-phase pumping operation. This degradation becomes increasingly severe and abrupt as pump specific speed falls, and is chiefly due to the reduced impeller performance. Degradation depends primarily on specific speed and pump geometry, void fraction and flow coefficient. Degradation also depends on flow regime, fluid viscosity, flow rate and system pressure. The evidence suggests that transient pump performance can be accurately predicted by steady-state tests.A pseudo-two-dimensional analysis is then presented of two-phase flow through a centrifugal pump to predict the head and torque performance over the full range of operating conditions. The loss of performance in the impeller in pumping operation is caused by the large slip that develops between the two phases as the gas slows dramatically compared to the liquid, particularly in stratified flow. In these conditions there is little or no pressure recovery by diffusion in the pump casing, with further energy losses at the impeller exit due to flow impact against the casing.The head and torque performance predicted by the model compared favourably with the results from the single-phase and two-phase experimental pump tests. The comparisons cover all 4 quadrants of pump operation over the whole voidage range for a comprehensive range of pump designs and fluid mixtures. A number of recommendations are made to improve two-phase pump performance for industrial applications.