Droplet microfluidics (DMF) is a fluidic handling technology that enables precision control over dispensing and subsequent manipulation of droplets in the volume range of microliters to picoliters, on a micro-fabricated device. There are several different droplet actuation methods, all of which can generate external stimuli, to either actively or passively control the shape and positioning of fluidic droplets over patterned substrates. In this review article, we focus on the operation and utility of electro-actuation-based DMF devices, which utilize one or more micro-/nano-patterned substrates to facilitate electric field-based handling of chemical and/or biological samples. The underlying theory of DMF actuations, device fabrication methods and integration of optical and opto-electronic detectors is discussed in this review. Example applications of such electro-actuation-based DMF devices have also been included, illustrating the various actuation methods and their utility in conducting chip-based laboratory and clinical diagnostic assays.