We are surrounded by structures that move and interact with a fluid — a flag flaps in a stiff breeze, a bird flies overhead, or a microscopic bacterium swims across a droplet of water. The study of how such immersed bodies interact with fluids has a long and interesting history, and defines a class of “moving boundary problems” that are central to science. What makes such problems especially difficult, and so fascinating for an applied mathematician, is that the dynamics of body and fluid are intimately intertwined and must be treated in an integrated way. I will discuss fluid-structure interactions ranging those we can directly see, like flapping flags and flying birds — to those we cannot, such as collective behaviors of swimming microbes and the transport of structures in biological cells. These examples will make clear the absolutely fundamental role that size plays in organizing our understanding.