The computation of realistic images requires the accurate simulation of radiant energy exchanges in a scene. The algorithms used to conduct such simulations are usually not restricted to visible light, thus the development of efficient computational techniques is of interest for a wide variety of applications (infrared and radar imaging, radio propagation etc.). Most current realistic rendering algorithms are based either on a deterministic, finite-element type approach (for instance, the radiosity method) or on a stochastic process (Monte Carlo methods). Recent advances in this field have promoted the use of hierarchical data structures and algorithms to represent radiant exchanges at different resolutions. The ability to always select the level of representation most appropriate for each phase of the simulation yields an impressive reduction of the total computational expense for a given accuracy level. Significantly, it also creates truly progressive algorithms that can produce an approximate solution in a very short time, and continuously improve it over time. This documents summarizes a STAR lecture, and presents several hierarchical algorithms in the context of the radiosity method. The most recent clustering techniques, allowing the simulation of very complex scenes, are reviewed. Pending research issues are identified and discussed, in particular the difficult question of error control for hierarchical methods.