The internal flows within single drops levitated in air have been experimentally examined on Earth and under low-gravity conditions. The motivation for this study is provided by the need to assess the impact of the levitation fields: Can a quiescent undisturbed state be reached when a liquid sample is electrostatically or ultrasonically levitated on Earth? The usefulness of the containerless experimentation methods for free drops and bubbles can only be rigorously established if the potential interfering effects associated with levitation do not significantly alter the characteristics of the phenomena under investigation. For example, in the case of the thermocapillary flows generated within a free drop by laser spot heating, the background flow within the unheated drop in an isothermal environment must be characterized first. Using both ultrasonic and electrostatic levitation techniques, we have developed the ability to stably hold single drops and to observe the internal flows under laser spot-heating. The fluid motion under the action of both natural buoyancy and surface tension gradients are three dimensional and asymmetrical, even though the heating is centered on the equator of the levitated drop. In addition, the asymmetrical heat distribution also induces rotation of the drop, especially when ultrasonic levitation is used. In order to eliminate the buoyant contribution, low-gravity experiments are under consideration. Initial space-based investigations using an ultrasonic device have revealed that any residual interference from acoustically-induced stresses and flows are eliminated when the sound power is reduced to a very low level. These data also show, however, that a 6 mm diameter drop remains very sensitive to aerodynamic drag exerted by even very slow circulation. This drag constitutes an effective torque driving the drop into slow solid-body rotation.