In recent years a new theory of the evolution of drainage networks and associated landscapes has emerged, mainly in connection with the development of fractal geometry and of self-organized criticality (SOC) concepts. This theory has much improved our understanding of the mechanisms which determine the structure of natural landscapes and their dynamics of evolution. In the first part of this paper the main ideas in the theory of landscape self-organization are outlined, and some remarkable features of the resulting structures are presented. In the second part we apply theoretical tools developed in the context of multifractal fields to the study of the scaling properties of the field of elevations of SOC landscapes. We observe that such landscapes appear to be more complex than simple self-affine fractals, although in some cases a simple fractal framework may be adequate for their description. We also show that multiple scaling may emerge as a result of heterogeneity in the field properties reflecting climate and geology. ¿ American Geophysical Union 1994