Level-of-detail (LOD) techniques have been studied for many years in computer graphics. Research in this area has reached maturity and several effective tools in LOD modeling are now available. However, most models and tools proposed in the literature are oriented to rendering. This is just one among many tasks that LOD should support in the context of applications involving geometric meshes of large size. Our approach to the research on LOD has always been to develop models and data structures that can support a range of spatial queries, rather than being optimized for rendering. Here, we present a historical overview, by highlighting the impact of this approach in the design of LOD models and data structures, and we briefly describe our current research, outlining new challenges in which LOD finds important applications.