This paper presents STORX: Shape and Topology Optimization for Research and Experimentation, an open-source MATLAB-based educational framework for learning and teaching computational design optimization. Unlike existing educational codes, which are typically built around a single formulation, STORX is, to the best of our knowledge, the first open-source MATLAB framework to unify parametric shape, level-set shape, and multiple families of topology optimization. All modules in STORX follow a consistent object-oriented structure and integrate visualization, sensitivity analysis, and finite element routines, enabling users to explore the continuum between shape and topology optimization in a transparent and reproducible manner. The code is designed to complement graduate-level coursework and independent research by emphasizing modularity and extensibility through a clear separation of intent. Core software interfaces are defined via abstract base classes, enabling new objective functionals and design/manufacturing constraints to be implemented by adding derived classes without modifying the core code. The paper also describes the software architecture and demonstrates how the framework maps mathematical formulations directly to executable code through a series of illustrative problems.

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