In this research chapter, we will present a software toolbox called EXOTica that is aimed at rapidly prototyping and benchmarking algorithms for motion synthesis. We will first introduce the framework and describe the components that make it possible to easily define motion planning problems and implement algorithms that solve them. We will walk you through the existing problem definitions and solvers that we used in our research, and provide you with a starting point for developing your own motion planning solutions. The modular architecture of EXOTica makes it easy to extend and apply to unique problems in research and in industry. Furthermore, it allows us to run extensive benchmarks and create comparisons to support case studies and to generate results for scientific publications. We demonstrate the research done using EXOTica on benchmarking sampling-based motion planning algorithms, using alternate state representations, and integration of EXOTica into a shared autonomy system. EXOTica is an open-source project implemented within ROS and it is continuously integrated and tested with ROS Indigo and Kinetic. The source code is available at https://github.com/ipab-slmc/exotica and the documentation including tutorials, download and installation instructions are available at https://ipab-slmc.github.io/exotica.