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To optimize their survival strategies many microorganisms use a variety of different swimming mechanisms, which often rely on the use of cellular appendages, such as flagella or cilia. In this chapter, we revisit different models for the hydrodynamics of cell swimming, including the paradigmatic squirmer model and Taylor's swimming sheet. We further discuss the impact of noise and biophysical reorientation mechanisms on their dynamics and elucidate their hydrodynamic interactions with nearby boundaries, which have different material properties, and other agents. We also address different active transport phenomena in non-Newtonian fluids, in the presence of external forces, gradients, and flows. Finally, we comment on examples of how microorganisms and mammalian cells stir their surrounding fluid to achieve different biological functions.

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