Microfluidic devices without walls have many advantages over channel-based devices. In droplet-based (“digital”) microfluidics, liquids are transported as droplets between parallel plates, rather than as streams. The droplets are created, moved, joined and divided by applying electrical potentials sequentially between electrodes buried beneath a hydrophobic dielectric layer. The resulting device is completely reconfigurable. Samples can be processed in series or simultaneously, each in the same way or through a unique sequence of steps. We have found shown that droplets of a wide range of liquids can be actuated by electrowetting, dielectrophoresis, or a combination of the two. An electromechanical model has been developed that explains the relative ease with which different liquids can be actuated and provides the basis for designing devices and operating conditions for actuating particular liquids. Applications of droplet microfluidics include separations by precipitation, solid phase extraction and liquid-liquid phase transfer. Understanding and controlling these processes represent significant new challenges to the modeling community.