The discovery in the late 1960s of the linear heat flow-heat production relationship was a major advance in the understanding of the thermal structure of continents. However, although heat flow provinces have now been defined in all continents except Antarctica, the full implications of the relationship to deep thermal structure and the limitations of the relationship to applications in all terranes are not yet clear. In addition, despite major advances in the geochemical factors controlling the distribution of heat production in the crust, a geochemical rationale for the relationship is lacking. The relationship was originally interpreted in terms of one-dimensionl models, but new two- and three-dimensional model studies suggest more complex interpretations in terms of lower crustal heat flow. Contributions to these problems in this special issue represent new observational, geochemical and modeling studies of the relationship and a renewed attempt to understand the thermal and geochemical implications of the relationship. ¿ American Geophysical Union 1987