A review is made of the simplest theory of the wake, with a more detailed description of vortex roll-up that has been available. This more complete description of the wake is in agreement with experimental results and may be used to illustrate several problems that face the experimentalist in the interpretation of his data. Once the roll-up problem has been discussed, the ways in which trailing vortex systems may be dissipated are reviewed. A system for evaluating the danger potential of aircraft wakes is discussed, and the wake characteristics of a representative selection of present-day aircraft are presented in terms of this method of classifying aircraft wakes.