One of the most challenging and important problems that the science and engineering communities are facing today -- and even more so in the future -- are representing, visualizing, and interpreting very large data sets. Very large data sets result from computer simulations of complex physical phenomena e.g., climate modeling, ocean modeling) or from high-resolution imaging e.g., satellite imaging, medical imaging). The technology currently being used to represent extremely large data sets is inappropriate for interactive, efficient, and detailed data analysis and visualization. It is impossible for a user of a visualization system to ``navigate'' through a data set consisting of millions of points and analyze it entirely. In this talk, I will present my ideas and my vision to overcome some of the problems associated with the representation of very large data sets. I will point out the necessity to bring together ideas from approximation theory and geometric modeling (splines), computational geometry (tesselations), and other related fields. The main themes of this talk will be possible avenues for representing large data sets by various hierarchies that facilitate data visualization at various levels of detail.