Optical lenses with electrically controllable focal length are of growing interest, in order to reduce the complexity, size, weight, response time and power consumption of conventional focusing/zooming systems, based on glass lenses displaced by motors. They might become especially relevant for diverse robotic and machine vision-based devices, including cameras not only for portable consumer electronics (e.g. smart phones) and advanced optical instrumentation (e.g. microscopes, endoscopes, etc.), but also for emerging applications like small/micro-payload drones and wearable virtual/augmented-reality systems. This paper reviews the most widely studied strategies to obtain such varifocal “smart lenses”, which can electrically be tuned, either directly or via electro-mechanical or electro-thermal coupling. Only technologies that ensure controllable focusing of multi-chromatic light, with spatial continuity (i.e. continuous tunability) in wavefronts and focal lengths, as required for visible-range imaging, are considered. Both encapsulated fluid-based lenses and fully elastomeric lenses are reviewed, ranging from proof-of-concept prototypes to commercially available products. They are classified according to the focus-changing principles of operation, and they are described and compared in terms of advantages and drawbacks. This systematic overview should help to stimulate further developments in the field.