The marching cubes [7,15] method demonstrated that isosurface extraction can be reduced, using a divide-and-conquer approach, to solving a local triangulation problem. In addition, the marching cubes method proposed a simple and efficient local triangulation using a lookup table. However, the marching cubes did not address the divide portion of the approach, i.e., how to efficiently search a large dataset for these small local triangulations. To this end, the marching cubes method checks each and every cell of the dataset.In this chapter, we introduce the three main approaches to accelerate isosurface extraction, (Section 2.2) and present two specific methods. Section 2.3 introduces the Span Space metaphor and uses it to devise a near-optimal search method in Section 2.4. Finally, Section 2.5 examines the view-dependent extraction approach and presents a particular implementation.