Phytoplankton moving in the ocean, spermatozoa making their way through the female reproductive tract and harmful bacteria that form biofilms on implanted medical devices interact with a surrounding fluid. Their length scales are small enough so that viscous effects dominate inertial effects allowing the resulting fluid dynamics to be described by the linear Stokes equations. However, nonlinear behavior can occur because these structures are flexible and their form evolves with the flow.In addition, the fluid environment may also be complex because of embedded microstructures that further complicate the dynamics.We will discuss recent successes and challenges in describing these elastohydrodynamic systems.