The rapid and safe transportation of suspended payloads with aerial vehicles is a crucial task across a breadth of industries, from construction to cargo delivery to agriculture to first response. As opposed to carrying payloads that are tightly secured against vehicles' bodies, manipulating payloads via a cable suspension allows the vehicle retain its agility and interact with objects from a distance. This problem has been studied for a variety of unmanned aerial vehicles (UAVs), including fixed-wing, helicopter, and quadrotor systems, in single- and multi-robot contexts. However, past work has focused predominantly on payload stabilization and elimination of the load swing during flight. This strategy is safe, but sub-optimal and overly conservative, and compromises UAVs' agility. In contrast, skilled pilots are able to achieve faster maneuvering by anticipating the effects of and allowing for load swings that naturally arise from the system's dynamics. This work proposes techniques for dynamic manipulation of slung-loads---execution of maneuvers where the payload swings significantly from the vertical orientation---with aerial robots. It begins by addressing the challenge of controlling suspended payloads at large excursions from the vertical configuration. It will then present a trajectory generation algorithm for a single quadrotor carrying a payload through obstacle-filled environments. In allowing the system to exploit its entire range of motion, rapid load transport and, more importantly, navigation of obstacles infeasible for swing-free systems can be achieved. Finally, it will propose a safe, scalable, and complete algorithm that generates trajectories for a multi-robot team in which each agent is transporting a single payload. Robots are coordinated such that they can safely execute simultaneous payload swings.