M.C. Escher's artwork has inspired and arguably even informed computer science, as well as geometric and shape modeling. Even today, much of his work poses challenges to conventional digital shape modeling systems. The authors introduce several interesting problems presented by Escher's graphic artworks and describe their use of a novel approach, based on implicit surfaces and their extension (Function Representation), to produce 2D, 2.5D and 3D computer models. They also discuss several physical objects or sculptures based on these models, crafted using digital fabrication processes.