  Microorganisms such as bacteria often swim in fluid environments that cannot
be classified as Newtonian. Many biological fluids contain polymers or other
heterogeneities which may yield complex rheology. For a given set of boundary
conditions on a moving organism, flows can be substantially different in
complex fluids, while non-Newtonian stresses can alter the gait of the
microorganisms themselves. Heterogeneities in the fluid may also be
characterized by length scales on the order of the organism itself leading to
additional dynamic complexity. In this chapter we present a theoretical
overview of small-scale locomotion in complex fluids with a focus on recent
efforts quantifying the impact of non-Newtonian rheology on swimming
microorganisms.
