This paper discusses the problem of matching models of curvilinear configurations to hand-drawn sketches. It collects observations from our own recent research, which focused initially on the domain of sketched human stick figures in diverse postures, as well as related computer vision literature. Sketch recognition, i.e., labeling strokes in the input with the names of the model parts they depict, would be a key component of higher-level sketch understanding processes that reason about the recognized configurations. A sketch recognition technology must meet three main requirements. It must cope reliably with the pervasive variability of hand sketches, provide interactive performance, and be easily extensible to new configurations. We argue that useful sketch recognition may be within the grasp of current research, if these requirements are addressed systematically and in concert.