Many microorganisms and cells function in complex (non-Newtonian) fluids, which are mixtures of different materials that exhibit both viscous and elastic stresses. For example, mammalian sperm swim through cervical mucus on their journey through the female reproductive tract, and they must penetrate the viscoelastic gel outside the ovum to fertilize. In micro-scale swimming the dynamics emerge from the coupled interactions between the complex rheology of the surrounding media and the passive and active body dynamics of the swimmer.  We use computational and analytical models of swimmers in viscoelastic fluids to investigate and provide mechanistic explanations for emergent swimming behaviors. I will discuss a few examples that highlight the role of fluid elasticity in micro-organism locomotion.