Bacteria predate plants and animals by billions of years. Today, they are the world's smallest cells yet they represent the bulk of the world's biomass, and the main reservoir of nutrients for higher organisms. Most bacteria can move on their own, and the majority of motile bacteria are able to swim in viscous fluids using slender helical appendages called flagella. Low-Reynolds-number hydrodynamics is at the heart of the ability of flagella to generate propulsion at the micron scale. In fact, fluid dynamic forces impact many aspects of bacteriology, ranging from the ability of cells to reorient and search their surroundings to their interactions within mechanically and chemically-complex environments. Using hydrodynamics as an organizing framework, we review the biomechanics of bacterial motility and look ahead to future challenges.