An important class of microscale fluid-structure interactions in biology involves the interactions and deformations of flexible elastica, both passive and active, with fluid flows. Examples range from fundamental biological transport processes such as the swimming of microorganisms using internally actuated cilia or flagella, the transport of material by the coordinated action of ciliary carpets to the involvement of both actuated and passive flexible filaments in the symmetry-breaking of vertebrates. 

I will present a broad overview of these problems and then discuss two problems concerning the dynamics of fibers in flows. First, I will talk about the novel buckling instabilities and complex shapes of single actin polymers in simple flows and their importance in the rheology of complex fluids. I will then discuss a coarse-grained continuum theory to understand the emergence of cytoplasmic streaming in the Drosophila (fruit-fly) egg cells, which is another striking example of fluid-structure interactions within living cells. Using this model, I will explain how large-scale circulatory flows emerge in these egg cells, how streamline topology is influenced by the geometry of cells, and speculate on possible cellular functions for such emergent flows.