The deluge of images on the Web has led to a number of efforts to organize images semantically and mine visual knowledge. Despite enormous progress on categorizing entire images or bounding boxes, only few studies have targeted fine-grained image understanding at the level of specific shape contours. For instance, beyond recognizing that an image portrays a cat, we may wish to distinguish its legs, head, tail, and so on. To this end, we present ShapeLearner, a system that acquires such visual knowledge about object shapes and their parts in a semantic taxonomy, and then is able to exploit this hierarchy in order to analyze new kinds of objects that it has not observed before. ShapeLearner jointly learns this knowledge from sets of segmented images. The space of label and segmentation hypotheses is pruned and then evaluated using Integer Linear Programming. Experiments on a variety of shape classes show the accuracy and effectiveness of our method.