The fluid dynamics video shows rigid, spatially asymmetric bodies interacting with oscillating background flows. A free rigid object, here a hollow "pyramid," can hover quite stably against gravity in the oscillating airflow with a zero mean, when its peak speed is sufficiently high. We further show in shadowgraph imaging how this asymmetric body sheds vortices in such an unsteady flow, thus enabling the body to "ratchet" itself through the background flow.