Many of today's recognition approaches for hand-drawn sketches are feature-based, which is conceptually similar to the recognition of hand-written text. While very suitable for the latter (and more tasks, e.g., for entering commands), such approaches do not easily allow for clustering and segmentation of strokes, which is crucial to their recognition. This results in applications which do not feel natural but impose artificial restrictions on the user regarding how diagrams and single components are to be drawn.In this paper we propose a recognition approach based on models, which is designed for the mentioned issue of clustering and segmentation. All strokes are fed into different models, where each model is responsible for a certain type of primitive, e.g., a line or an arc. The recognition of a component in the drawing is then decomposed into the recognition of its primitives, which can be directly searched for in the models. Finally, the identified primitives are assembled to the complete component.In several case studies we also show the applicability and generality of our approach, as very different types of components can be recognized. Furthermore, the proposed approach is part of a complete system to sketch understanding which can not only recognize single components, but can also reason about diagrams as a whole, consisting of a set of these components.