The interaction of flowing fluids with free bodies -- sometimes
compliant, sometimes active, sometimes multiple -- constitutes a class
of beautiful dynamic boundary problems that are central to biology and
engineering. Examples range from how organisms locomote in fluids
(which depends strongly on scale) to how non-Newtonian stresses
develop in complex liquids (strongly dependent on the nature of
fluidic microstructure). I will discuss several interesting examples,
emphasizing how they are formulated mathematically so as to yield
models tractable for analysis or simulation, and show how this work
has interacted with experimental studies.