A simple discussion of electron cooling theory, with emphasis on relativistic scaling relations, is given. This discusion is used to predict the behaviovr of electron cooled beams, subjected also to an internal target and to intrabeam scattering. Technical considerations relating to the alignment and the confinement of electron beams for cooling indicate that the longitudinal magnetic field will be abandoned in favour of focusing by discrete lenses at electron energies above about 1 MeV. The experiments on acceleration, transport, and collection of prototype electron beams made at Novosibirsk and Wisconsin are discussed. It is concluded that intermediate energy electron cooling is within the capability of present technology, and although its most important application may be for improving the luminosity of colliders, nuclear and particle physics applications requiring high energy, spatial, or time resolution also may benefit.