In this paper we consider the problem of object parsing, namely detecting an object and its components by composing them from image observations. Apart from object localization, this involves the question of combining top-down (model-based) with bottom-up (image-based) information. We use an hierarchical object model, that recursively decomposes an object into simple structures. Our first contribution is the formulation of composition rules to build the object structures, while addressing problems such as contour fragmentation and missing parts. Our second contribution is an efficient inference method for object parsing that addresses the combinatorial complexity of the problem. For this we exploit our hierarchical object representation to efficiently compute a coarse solution to the problem, which we then use to guide search at a finer level. This rules out a large portion of futile compositions and allows us to parse complex objects in heavily cluttered scenes.