Digital microfluidics is the second-generation lab-on-a-chip architecture based upon micromanipulation of droplets via a programmed external electric field by an individually addressable electrode array. Dielectrophoresis (DEP) and electrowetting-on-dielectric (EWOD) are of the dominant operating principles. The microfluidic mechanics of manipulating electrified droplets are complex and not entirely understood. In this article, EWOD and DEP are analyzed both analytically and numerically under a unified framework of droplet electrohydrodynamics (EHD). The numerical simulations based on droplet EHD are first validated against analytical and experimental results and have achieved a good agreement both quantitatively and qualitatively. Simulations are then used extensively in this article to illustrate device operation, to expose underlying physics, and to confirm our conclusions.