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Microorganisms live in a world of low Reynolds number where viscous forces dominate. The absence of inertia imposes stringent constraints on the types of effective locomotion strategies in the microscopic world. In addition, biological fluids, such as respiratory and cervical mucus, typically display complex rheological properties such as viscoelasticity and shear-thinning viscosity. The fundamental question whether these nonlinear rheological properties enhance or hinder locomotion at small scales has attracted considerable attention recently. In this talk, we will consider different idealized models to elucidate how non-Newtonian fluid rheology influences propulsion at low Reynolds number, and discuss the possibilities of exploiting these complex fluid properties in the design of artificial micro-propellers.