A survey is provided of a variety of problems where a passive or an active drop experiences directed motion consequence of the action of an external or internal agent or a combination of both. An active drop is capable of reacting by engendering autonomous, self-propelled motion in favor or against the agent. The phenomena involved offer diverse complexity but one way or another the drop motion finally rests on thermo- or soluto-capillarity hence on interfacial tension gradients. Accordingly, here a minimal mathematical framework underlying such drop motions is provided when direct external temperature or solute gradients, illumination, internal heat generation or surface chemical reaction are incorporated into the physico-chemical-hydrodynamics. Display omitted •Review of hydrodynamics of passive and active drops/bubbles in host fluids.•Mathematical description of the motion of drops/bubbles due to interfacial tension gradients is itemized.•Force on active and passive drops/bubbles has been provided.•Classical and recent experiments on active and passive motion of drops/bubbles are described.