At the present time several hundred hydrofoilcraft are in service throughout the world. The upsurge in the use of these craft did not really begin until the late 1950s, although fascination with the idea of supporting small boats with underwater wings dates well back into the nineteenth century. About the turn of the century, hydrofoil flight was achieved, to be followed in a few years by Bell and Baldwin who, at the close of World War I, achieved the modern hydrofoil speed of 60 knots in a very novel craft. Progress and interest in this form of transportation then waned for many years. There were some interesting developments just prior to and through World War II in Europe, and after the war interest quickened in several countries. Current thinking at this time may be judged by Gabdelli & von Karman (1950), who note that the drag of surface vessels may be decreased by lifting the floating structure with hydrofoils. But they go on to add that they ... do not attempt to estimate the effect of such a radical innovation; whether the trials until now appear promising is a question of individual judgment. As subsequent events have proven, the trials were indeed promising. The many hydrofoil craft now in service are of several different types and a number of more advanced concepts are being developed swiftly. Greater speed in all forms of transportation has always been sought, provided the price is not too great. The air-sea surface is a particularly inhospitable environment for major advances in operating speed, yet it is partly this advance that is the stimulus for hydrofoil craft as well as that for conventional marine craft and the newer hover craft. Silverleaf (1970) and Silverleaf & Cook (1970) review all these recent developments from technical and economic standpoints. High speeds at sea are now possible, they observe, but may not be attained for lack of naval or commercial demands. The successful achievements of hydrofoil craft to date and the possibility of high speeds at sea are due to the greatly increased understanding in recent years of the flow past hydrofoils and also to the development of foil configurations and control systems for coping with the roughness of the sea surface. It seems appropriate, therefore, in this review to link the discussion of hydrofoils with that of progress in the craft, for the two are very interdependent. This interaction has been the source of a great deal of research in applied fluid mechanics in recent years. The methods of analysis, experiment, and design in this field follow closely those in aeronautics, yet there are some important differences because of the medium itself. These include the phenomena due to the free surface (an ever-present boundary in naval hydrodynamics) and the possibility of a phase change through cavitation or ventilation with consequent important modification of the flow; because the liquid density is so much greater than in equivalent aeronautical applications, the dynamic response to motions must be treated very carefully. Hydrofoils, in addition, find application as control surfaces and structural members in marine craft generally, and serve also as elements of propulsion devices. In what follows, the general characteristics of hydrofoil craft are briefly reviewed together with some representative modern examples. Some physical aspects of the flow past hydrofoils are then described, followed by a resume of some of the recent methods used in design and analysis of hydrofoils. In this short account several important topics have of necessity been omitted; these include propulsion, hydroelastic problems, and ship motions, each of which could serve as the topic of a separate article.