Online sketch recognition uses machine learning and artificial intelligence techniques to interpret markings made by users via an electronic stylus or pen. The goal of sketch recognition is to understand the intention and meaning of a particular user's drawing. Diagramming applications have been the primary beneficiaries of sketch recognition technology, as it is commonplace for the users of these tools to rst create a rough sketch of a diagram on paper before translating it into a machine understandable model, using computer-aided design tools, which can then be used to perform simulations or other meaningful tasks. Traditional methods for performing sketch recognition can be broken down into three distinct categories: appearance-based, gesture-based, and geometric-based. Although each approach has its advantages and disadvantages, geometric-based methods have proven to be the most generalizable for multi-domain recognition. Tools, such as the LADDER symbol description language, have shown to be capable of recognizing sketches from over 30 different domains using generalizable, geometric techniques. The LADDER system is limited, however, in the fact that it uses a low-level recognizer that supports only a few primitive shapes, the building blocks for describing higher-level symbols. Systems which support a larger number of primitive shapes have been shown to have questionable accuracies as the number of primitives increase, or they place constraints on how users must input shapes (e.g. circles can only be drawn in a clockwise motion; rectangles must be drawn starting at the top-left corner). This dissertation allows for a significant growth in the possibility of free-sketch recognition systems, those which place little to no drawing constraints on users. In this dissertation, we describe multiple techniques to recognize upwards of 18 primitive shapes while maintaining high accuracy. We also provide methods for producing confidence values and generating multiple interpretations, and explore the difficulties of recognizing multi-stroke primitives. In addition, we show the need for a standardized data repository for sketch recognition algorithm testing and propose SOUSA (sketch-based online user study application), our online system for performing and sharing user study sketch data. Finally, we will show how the principles we have learned through our work extend to other domains, including activity recognition using trained hand posture cues.