Welcome to MATWA: the Matching Algorithm Toolkit Web Application, developed at the University of Glasgow, School of Computing Science by 20+ contributors over 20+ years. This application provides an interface to access implementations of almost 40 algorithms to compute matchings and associated structures in instances of matching problems with ordinal preferences. The tool was demoed at AAAI 2025 (see the associated proceedings paper here and an extended version here). Support is provided via pop-ups activated from the bottom-right of each selection panel, and via the User Guide.