  Many microorganisms live and evolve in complex fluids. Examples include
mammalian spermatozoa in cervical mucus, worms (e.g., \textit{C. elegans}) in
wet soil, and bacteria (e.g., \textit{H. pylori}) in our stomach lining. Due to
the presence of (bio)polymers and/or solids, such fluids often display
nonlinear response to (shear) stresses including viscoelasticity and shear-rate
dependent viscosity. The successful interaction between these microorganisms
and their fluid environment is critical to the function of many biological
processes including human reproduction, ecosystem dynamics, and the spread of
disease \& infection. This interaction is often nonlinear and can lead to many
unexpected behavior. Here, I will discuss developments in characterizing,
modeling, and understanding the swimming behavior of model microorganism in
viscoelastic and shear-thinning fluids. Three main microorganisms will be
explored: (i) the nematode \textit{C. elegans}, an undulatory swimmer; (ii) the
green algae \textit{C. reinhardtii}, a puller swimmer; and (iii) the bacterium
\textit{E. coli}, a pusher swimmer. Investigation with artificial
particles/swimmers will also be discussed; such studies are helpful in
decoupling the biology from hydrodynamic effects. We will explore the
interactions between these swimmers' gaits, geometry, and actuation and fluid
rheological behavior using mostly experiments, and discuss these results
relative to numerical and analytical predictions.
