A synthetic approach to the problem of the adhesive contact of axisymmetric elastic bodies is proposed. A convenient and general formulation is thus obtained, which is shown to yield directly most of the useful models. In particular, the roles of the shape of the indenter on the one hand, and of the nature of the attractive interactions on the other hand are clearly separated. By nature, this approach can also be used in the case where the bodies are in interaction but not in contact. This results in a consistent treatment of long-range interactions and contact properties.