Abstract: Problems in biological fluid dynamics typically involve the interaction of an elastic structure with the surrounding fluid. Examples of these coupled fluid-structure systems include blood flow in the heart, air flow through the lungs, and sperm motility in the reproductive tract. These biological processes can each be described by a system of time-dependent, coupled, nonlinear partial differential equations. While the explicit solution of these complex equations is impossible, scientists are making progress in understanding these systems using computational methods. In this talk, we will present an overview of biological fluid dynamics, and discuss the interdisciplinary nature of the research in this field. We will focus on the examples of ciliary and flagellar beating in microorganisms, and the swimming of nematodes and leeches.