Level set models combine a low-level volumetric representation, the mathematics of deformable implicit surfaces, and powerful, robust numerical techniques to produce a novel approach to shape design. While these models offer many benefits, their large-scale representation and numerical requirements create significant challenges when developing an interactive system. This paper describes the collection of techniques and algorithms (some new, some pre-existing) needed to overcome these challenges and to create an interactive editing system for this new type of geometric model. We summarize the algorithms for producing level set input models and, more importantly, for localizing/minimizing computation during the editing process. These algorithms include distance calculations, scan conversion, closest point determination, fast marching methods, bounding box creation, fast and incremental mesh extraction, numerical integration, and narrow band techniques. Together these algorithms provide the capabilities required for interactive editing of level set models.