The interaction of light and matter in the world surrounding us is of striking complexity and beauty. Since the very beginning of computer graphics, adequate modelling of these processes and efficient computation is an intensively studied research topic and still not a solved problem. The inherent complexity stems from the underlying physical processes as well as the global nature of the interactions that let light travel within a scene. This paper reviews the state of the art in interactive global illumination (GI) computation, i.e., methods that generate an image of a virtual scene in less than 1 s with an as exact as possible, or plausible, solution to the light transport. Additionally, the theoretical background and attempts to classify the broad field of methods are described. The strengths and weaknesses of different approaches, when applied to the different visual phenomena, arising from light interaction are compared and discussed. Finally, the paper concludes by highlighting design patterns for interactive GI and a list of open problems.