This review paper summarizes various aspects of directive beaming and explains these aspects in terms of leaky waves. Directive beaming occurs in antenna design where a narrow beam is obtainable by using fairly simple planar structures excited by a single source. These structures include Fabry-Pérot cavity structures as well as metamaterial structures made from artificial low-permittivity media. Directive beaming also occurs in the optical area where it has been observed that highly directive beams can be produced from small apertures in a metal film when an appropriate periodic patterning is placed on the film. One aspect that these phenomena all have in common is that they are due to the excitation of one or more weakly attenuated leaky waves, the radiation from which forms the directive beam. This is established in each case by examining the role of the leaky waves in determining the near-field on the aperture of the structure and the far-field radiation pattern of the structure.