This paper reports recent research efforts to advance the functionality of Unmanned Aerial Vehicles (UAVs) beyond passive observation to active interaction with and manipulation of objects. The archetypical aerial manipulation task — grasping objects during flight — is difficult due to the unstable dynamics of rotorcraft and coupled object-aircraft motion. In this paper, we analyze key challenges encountered when lifting a grasped object and transitioning into laden free-flight. We demonstrate that dynamic load disturbances introduced by the load mass will be rejected by a helicopter with PID flight control. We determine stability bounds in which the changing mass-inertia parameters of the system due to the grasped object will not destabilize this flight controller. The conditions under which transient partial contact mechanics of objects resting on a surface will not induce instability are identified. We demonstrate grasping and retrieval of a variety of objects while hovering, without touching the ground, using the Yale Aerial Manipulator testbed.