Fluid dynamic principles that are fundamental to understanding the motion of fluids in radial compressors are highlighted. These include the continuity and the momentum equations in various forms. These equations are then used to delineate the effect of the fluid motion on pressure gradients on the flow. The simple radial equilibrium equation for a circumferentially averaged flow is introduced. Special features of the flow in radial compressors due to the radial motion are considered, such as the effects of the Coriolis and centrifugal forces. The relative eddy, which gives rise to the slip factor of a radial impeller, is explained. A short overview of boundary layer flows of relevance to radial compressors is provided. The flow in radial compressor impellers is strongly affected by secondary flows and tip clearance flows, and an outline is provided of the current understanding of the physics related to these. The phenomenon of jet-wake flow in compressors is described.