Ultrasonic and electrostatic levitation methods allow the detailed experimental investigation of the dynamics and transport processes associated with free single drops stably positioned in a fluid host. The response of these drops to artificially induced controlled stimuli can be recorded and analyzed to deduce some of their thermophysical properties, or to study the characteristics of the nonlinear dynamics of free three-dimensional liquid-gas interfaces. Earth-based levitation, however, requires high field intensities that introduce additional artifacts interfering with the analysis of the drop response. We have carried out experimental studies both at 1-G and in microgravity in order to refine techniques to quiescently position free drops in a gaseous host, and to examine the thermocapillary flows resulting from spot heating. Both spherical and drastically flattened levitated drops have been investigated at 1-G using electrostatic/ultrasonic hybrid levitation systems and spot heating from a focused CO2 laser. Thermocapillary flows in spherical drops at 1-G invariably couple with the overall drop rotational motion, while drastically flattened drops reveal more regular flow patterns in agreement with results from theoretical predictions for axisymmetric flows. Low-gravity investigations using a low-cost and compact experimental apparatus in the Shuttle Glovebox Facility have allowed the development of experimental methods for the quiescent positioning of free drops. A better understanding control of simple and compound drop rotation and of the impact of acoustic field positioning on drop internal flows has been obtained. Preliminary data on thermocapillary flows in free drops in microgravity have also been gathered.