Matching markets, in which agents are assigned to one another based on preferences and capacity constraints, are pervasive in various domains. This paper introduces MATWA (https://matwa.optimalmatching.com), a web application that offers the most comprehensive collection to date of algorithms for fundamental matching under preference problem classes. MATWA provides results of algorithm executions and visualisations of structural properties. It is intended to be a resource for the community of researchers, educators and practitioners, supporting experimentation, as well as aiding the understanding of matching algorithms.