We theoretically investigate the fluid mechanics of self-propelled (or swimming) bodies. An important factor concerning the hydrodynamics of locomotion concerns the relative strength of inertial to viscous forces experienced by the swimmer, the ratio of which is quantified by the Reynolds number, Re. Particular attention is given to the regime where Re is intermediate, where viscous and inertial forces are both relevant to fluid motion. We study two broad classes of swimmers: ‘pushers’ and ‘pullers’. Pushers produce thrust from the rear of their body, while pullers generate thrust from the front. We first investigate the near-field flow due to pushers and pullers by numerically solving the Navier-Stokes equations for Re of 0.01–1000. We show that, although the locomotion of pushers and pullers is similar at small Re, drastic differences due to fluid inertia arise as Re is increased. Most remarkably, flow instabilities develop at much smaller Re for a puller than a pusher. Further, we investigate the large scale fluid transport induced by a swimmer as a function of Re in the context of the induced ‘drift volume’. The drift volume quantifies the volume of fluid swept out by a ‘dyed’ fluid plane that is initially perpendicular to the body’s path. However, we first address the previously unsolved problem of the drift volume due to a body that is towed by an external force at finite Re. While the drift volume is comparable to the body volume in inviscid flow (Re ! 1), it is much larger when Re is finite due to viscous effects. The drift volume due to a swimmer is smaller than that due to a towed body because swimmers generate a weaker far-field flow. However, it is still potentially large compared to the volume of the swimmer’s body in the viscously dominated small-Re regime. However, the drift volume of a swimmer quickly diminishes as Re is increased.