Visual objects are composed of parts like a body, arms, legs and a head for a human or wheels, a hood, a trunk and a body for a car. This compositional structure significantly limits the representation complexity of objects and renders learning of structured object models tractable. Adopting this modeling strategy I describe a system, which both (i) automatically de-composes objects into a hierarchy of relevant compositions and which (ii) learns such a compositional representation for each category without supervision. Compositions are represented as probability distributions over their constituent parts and the relations between them. The global shape of objects is captured by a graphical model which combines all compositions. Experiments on large standard benchmark data sets underline the competitive recognition performance of this approach and they provide insights into the learned compositional structure of objects.