The advent of high-performance computing has completely transformed the nature of most scientific and engineering disciplines, making the study of complex problems from experimental and theoretical disciplines computationally feasible. All science and engineering disciplines are facing the same problem: how to archive, transmit, visualize, and explore the massive data sets resulting from modern computing. In the past, when only small amounts of data were processed, many researchers could accomplish some of these objectives at interactive rates on simple desktop machines. Today's impact problems of science and engineering require new algorithms for the analysis of the massive data sets produced by computational simulations and new sensor technology. The exploration of truly massive data sets requires new techniques in compression, storage, transmission, retrieval, and visualization, as the existing techniques for small data sets do not scale well, or not at all. New systematic approaches are needed to address the interrelated problems of storage, visualization, and exploration of these massive data sets. In this paper, we describe the use of recursive tetrahedral meshes based on longest edge bisection as a data structure for scientific visualization and its application to the approximation of datasets with material interfaces and interactive isosurface extraction from large volumetric datasets. The rest of this paper is structured as follows. Section 2 discusses previous work using longest edge bisection in the field of scientific visualization. Sections 3 and 4 detail the basic mesh refinement scheme and the adaptive refinement of the mesh. Section 5 discusses the application of this structure in the approximation of datasets that contain material interfaces. Section 6 describes its application to fast isosurface extraction from large datasets. Sections 7 and 8 give implementation details and Section 9 describes areas of future research.