The authors give I/O-optimal techniques for the extraction of isosurfaces from volumetric data, by a novel application of the I/O-optimal interval tree of Arge and Vitter (1996). The main idea is to preprocess the data set once and for all to build an efficient search structure in disk, and then each time one wants to extract an isosurface, they perform an output-sensitive query on the search structure to retrieve only those active cells that are intersected by the isosurface. During the query operation, only two blocks of main memory space are needed, and only those active cells are brought into the main memory, plus some negligible overhead of disk accesses. This implies that one can efficiently visualize very large data sets on workstations with just enough main memory to hold the isosurfaces themselves. The implementation is delicate but not complicated. They give the first implementation of the I/O-optimal interval tree, and also implement their methods as an I/O filter for Vtk's isosurface extraction for the case of unstructured grids. They show that, in practice, the algorithms improve the performance of isosurface extraction by speeding up the active-cell searching process so that it is no longer a bottleneck. Moreover, this search time is independent of the main memory available. The practical efficiency of the techniques reflects their theoretical optimality.