This paper reviews the hydrodynamics of copepods, guided by results obtained from recent theoretical and numerical studies of this topic to highlight the key concepts. First, we briefly summarize observational studies of the water flows (e.g., the feeding currents) created by copepods at their body scale. It is noticed that the water flows at individual copepod scale not only determine the net currents going around and through a copepod's hair-bearing appendages but also set up a laminar flow field around the copepod. This laminar flow field interacts constantly with environmental background flows. Theoretically, we explain the creation of the laminar flow field in terms of the fact that a free-swimming copepod is a self-propelled body. This explanation is able to relate the various flow fields created by copepods to their complex swimming behaviors, and relevant results obtained from numerical simulations are summarized. Finally, we review the role of hydrodynamics in facilitating chemoreception and mechanoreception in copepods. As a conclusion, both past and current research suggests that the fluid mechanical phenomena occurring at copepod body scale play an important role in copepod feeding, sensing, swarming, mating, and predator avoidance.