The concavity tree (c.t.) is an attractive way of representing the shape of a 2-dimensional object or silhouette. In this paper, the literature on the subject is briefly reviewed, the method of generating c.t.s is described and their properties discussed. The paper goes on to report original work on the use of c.t.s for matching shapes and for detecting certain features such as edge features and symmetry. Possible applications of c.t.s are briefly reviewed, leading to the conclusion that they could be a valuable aid in the inspection, sorting and manipulation of industrial artefacts.