A common class of fluid-structure interaction problems involves the dynamics of flexible fibers immersed in a Stokesian fluid. In biology, this topic arises in modeling the flagella or cilia involved in microorganism locomotion and mucal transport, in determining the shape of biofilm streamers, and in understanding how biopolymers such as microtubules respond to the active coupling afforded by motor proteins. In engineering, it arises in the paper-processing industry, where wood pulp suspensions can show an abrupt appearance of normal-stress differences, and in microfluidic engineering, where flow control using flexible particles has been explored. Over the past decade, the dynamics of immersed fibers has been studied intensively, particularly by theoretical means, while on the experimental side, recent advances in microfabrication and flow control have led to new insights. In this chapter we survey this work on the dynamics of flexible fibers in flows, including model experiments and the development of specialized numerical methods for simulating fiber dynamics in various flow situations.