In this dissertation we study the interactions between free bodies and unsteady viscous flows, with particular interest in locomotion and in particle transport in streaming flows.For self-propelling bodies, we present systems with two different mechanisms that generate locomotion. The first one obtains its propulsive force from vortex shedding that results from the spinning of a rotor internal to a hydrofoil. The second type of locomotion results from changes in shape of the system, similar to the deformations one sees in a fish as it swims. We present a set of swimmers whose configuration manifold exhibits the structure of a trivial principal fiber bundle. For such systems, locomotion can be obtained from cyclic actuation of the shape variables, as long as the corresponding closed loops in the manifold of body shapes enclose a certain kind of curvature. In the robotics literature, this curvature is typically obtained from an analytical model. We present a strategy to obtain the curvature of a system from experiments. We also study the performance of a swimmer with underactuated dynamics on the shape manifold. We show that single input actuation can enable locomotion comparable to that realized with full actuation in the shape variables. For particles in streaming flows, we concentrate on flows generated by oscillating cylinders in a viscous fluid. Particles in such flows get trapped in the centers of streaming cells. We explore strategies — with the aid of a low-order approximation and a high-fidelity model — to transport particles from a streaming cell near one cylinder to a streaming cell near another cylinder.