Electrowetting has become one of the most widely used tools for manipulating tiny amounts of liquids on surfaces. Applications range from 'lab-on-a-chip' devices to adjustable lenses and new kinds of electronic displays. In the present article, we review the recent progress in this rapidly growing field including both fundamental and applied aspects. We compare the various approaches used to derive the basic electrowetting equation, which has been shown to be very reliable as long as the applied voltage is not too high. We discuss in detail the origin of the electrostatic forces that induce both contact angle reduction and the motion of entire droplets. We examine the limitations of the electrowetting equation and present a variety of recent extensions to the theory that account for distortions of the liquid surface due to local electric fields, for the finite penetration depth of electric fields into the liquid, as well as for finite conductivity effects in the presence of AC voltage. The most prominent failure of the electrowetting equation, namely the saturation of the contact angle at high voltage, is discussed in a separate section. Recent work in this direction indicates that a variety of distinct physical effects—rather than a unique one—are responsible for the saturation phenomenon, depending on experimental details. In the presence of suitable electrode patterns or topographic structures on the substrate surface, variations of the contact angle can give rise not only to continuous changes of the droplet shape, but also to discontinuous morphological transitions between distinct liquid morphologies. The dynamics of electrowetting are discussed briefly. Finally, we give an overview of recent work aimed at commercial applications, in particular in the fields of adjustable lenses, display technology, fibre optics, and biotechnology-related microfluidic devices.