We summarize our research results in three main areas: coating flows; electrohydrodynamics of drops; and wetting and spreading of drops. Experimental, computational and analytical methods are used to address a variety of issues. Coating flow studies include the effect of roughness, surfactants, and adsorbed particles on the dynamics of dip-coating. Electrohydrodynamic studies include drop deformation in uniform electric fields, shape distortion due to charge convection in sedimenting drops, and driving chaotic advection by either an electric field inclined to the direction of drop motion or time-periodic changes in the direction of the electric field. Heat and mass transport from chaotically mixed droplets exhibit unexpected and remarkable increases in the rates of transport. Finally, we develop an analytical solution to the problem of a static droplet, and use numerical techniques to predict its migration due to surface tension gradients.