Matching markets, where 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 offering a rich collection of algorithms for fundamental problem models involving matching under preferences. MATWA provides results and visualizations of matching algorithm outputs based on different methods for providing problem instances. In this paper, we describe the features of the system, illustrating its usage for different problem models, and outlining the algorithm implementations that are supported. We also give evidence of usability testing and illustrate how the system was used to obtain new empirical results for a specific matching problem. MATWA is intended to be a resource for the community of researchers in the area of matching under preferences, supporting experimentation as well as aiding the understanding of matching algorithms.