Traditional user interfaces in modeling have followed the WIMP (Window, Icon, Menu, Pointer) paradigm. While functional and powerful, they can also be cumbersome and daunting to a novice user; creating a complex model requires much expertise and effort. A recent trend is toward more accessible and natural interfaces, which has lead to sketch-based interfaces for modeling (SBIM). The goal is to allow hand-drawn sketches to be used in the modeling process, from rough model creation through to fine detail construction. Mapping 2D sketches to a 3D modeling operation is a difficult and ambiguous task, so our categorization is based on how an SBIM application chooses to interpret a sketch, of which there are three primary methods: to create a 3D model, to add details to an existing model, or to deform and manipulate a model. In this STAR, we present a taxonomy of sketchbased interfaces focused on geometric modeling applications. The canonical and recent works are presented and classified, including techniques for sketch acquisition, filtering, and interpretation. The report also includes a discussion of important challenges and open problems for researchers to tackle in the coming years.