In this paper we present the 2D Shape Structure database, a public, user-generated dataset of 2D shape decompositions into a hierarchy of shape parts with geometric relationships retained. It is the outcome of a large-scale user study obtained by crowdsourcing, involving over 1200 shapes in 70 shape classes, and 2861 participants. A total of 41953 annotations has been collected with at least 24 annotations per shape. For each shape, user decompositions into main shape, one or more levels of parts, and a level of details are available. This database reinforces a philosophy that understanding shape structure as a whole, rather than in the separated categories of parts decomposition, parts hierarchy, and analysis of relationships between parts, is crucial for full shape understanding. We provide initial statistical explorations of the data to determine representative (" mean ") shape annotations and to determine the number of modes in the annotations. The primary goal of the paper is to make this rich and complex database openly available (through the website http://2dshapesstructure.github.io/index.html), providing the shape community with a ground truth of human perception of holistic shape structure.