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Life under the microscope is significantly different from our experiences in the macroscopic world. Inertial effects, which govern motion at the macroscopic world, become subdominant to viscous forces at small length scales. The Reynolds number (Re) quantifies the relative importance of inertial to viscous forces. Microorganisms, such as bacteria and spermatozoa, inhabit environments with typical Re between 10̄̄⁻⁵ and 10⁻². The absence of inertia imposes stringent constraints on the types of effective locomotion strategies. This also poses a fundamental challenge in designing synthetic swimmers and fluid transport systems at microscopic scales. Interestingly, microorganisms have evolved diverse strategies to achieve locomotion. This thesis is devoted to studying the fluid mechanics of biological and synthetic locomotion at low Reynolds number under three themes: swimming microorganisms, synthetic locomotion, and locomotion in complex fluids. The first theme focuses on using different idealized hydrodynamic models to study the swimming of microorganisms. Under this theme, we extend the classical Taylor's swimming sheet model to analyze the unsteady inertial effects in flagellar swimming. We also present a hydrodynamic investigation of an interesting double-wave structure observed in insect sperm flagella. We turn our attention to synthetic locomotion in the second theme. Different physical mechanisms are explored to design synthetic micro-swimmers, which have many potential biomedical applications, such as microsurgery and targeted drug delivery systems. Specifically, we exploit elasticity and extensibility of a body to design locomotion strategies. Finally, the third theme concerns locomotion in complex fluids. Most biological fluids are indeed polymeric and hence display non-Newtonian rheological properties. We investigate the idea of taking advantage of the nonlinear rheological properties of a complex fluid to enable locomotion otherwise impossible in a Newtonian fluid. Simple mechanisms are designed to exploit the non- Newtonian stresses for micropropulsion and micropumping. The results are also applied to developing a microrheological technique based on information from locomotion