The rapid development of biotechnology we are witnessing nowadays is strongly related to the advances in bioprocess engineering. This field of engineering, including both bioreactor engineering and down-stream processing, is an integration of biological, biochemical and engineering principles, leading to the quantitative description and development of biotechnological processes carried out on an industrial scale. A very important part of bioprocess engineering problems involves the fluid mechanics problems occurring in biotechnological equipment. These are both the problems related to bioreactor design and operation, and to down-stream processing operations, such as micro- and ultrafiltration, centrifugation, precipitation, extraction, sorptions, flocculation, mixing, fluid transportation, etc. This paper is focused mainly on fluid mechanical problems in bioreactor engineering. It begins with a brief reminder of some basic concepts in fluid flow, rheology and turbulence, of relevance to bioreactors. Then the main types of bioreactor design are reviewed, including stirred bioreactors and pneumatically driven bioreactors. The hydrodynamic characteristics of different types of reactors are then outlined, including power consumption, mixing, heat and mass transfer, aeration, and cell demage by hydrodynamic stresses. Finally, some new developments are discussed, including the use of computer fluid dynamics (CFD) to describe hydrodynamics of bioreactors, and the use of the multifractal theory of turbulence to describe some cell damaging effects.