This review of the hydrodynamics of stirred bioreactors begins with an introduction to the agitation problems of particular concern in such systems. This is followed by a brief review of some basic concepts in turbulence and rheology of relevance to bioreactors. Important aspects of single phase mixing in low viscosity, high viscosity and Theologically complex broths are then covered in some detail including flow patterns, power number versus Reynolds number plots (including the modification of the latter to allow for shear thinning broths), flow numbers, energy dissipation rates and flow close to impellers and between multiple impeller systems. From these basic principles, the problem of homogenization is then covered in depth because of its significance for bioreactor performance. Aeration concepts are then introduced and the behavior of traditional Rushton turbine impellers is then treated in detail, covering the flow patterns, aerated power characteristics, mixing time and scale-up considerations. The weaknesses of the Rushton turbine are then discussed which leads into a section describing how more modern impellers are able to improve on many of these, especially emphasising their ability to introduce more energy dissipation into the broth and handle more air before flooding, both of which enhance oxygen transfer. The improvement in bulk blending found with multiple axial flow agitators is brought out too. Finally, the retrofitting of fermenters originally containing Rushton turbines with these more modern impellers is discussed. In conclusion, it is clear that there have been substantial increases in the understanding of stirred bioreactor hydrodynamics. However, whilst further understanding will occur within the framework discussed here, the expectation must be that computational fluid dynamics will increase in importance in spite of the difficulty of handling complex rheology, multiphase systems and biological responses. This review article has 135 references.