The structure of the sampling and reconstruction process, as well as that of the scene and its data representation, can be utilised to effect significant benefits in global illumination algorithms. As an introduction, previous methods that have utilised this structure are reviewed and some possible improvements are suggested. A new framework is then introduced that utilises the concept of an oracle as an abstraction to provide information about the complex computational processes of global illumination. This framework is based on the recognition of the relevant aspects of scene structure, the description of the problems to be solved in terms of oracles, the use of structure to create approximations to the oracles, and finally techniques to monitor the cost, error and quality of the approximations. Each aspect of the framework is discussed in detail, presenting certain oracles that are useful for global illumination algorithms. Two examples of its application are presented. The first example is a simple local illumination problem, that allows us to consider several aspects of the oracle methodology. The second example uses the framework to enhance the progressive refinement radiosity based solution to global illumination. Both examples illustrate the benefits of the proposed framework. Finally, some suggestions are made for future research directions.