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Many object recognition systems are limited by their inability to share common parts or structure among related object classes. This capability is desirable because it allows information about parts and relationships in one object class to be generalized to other classes for which it is relevant. This ability has the potential to allow effective parameter learning from fewer examples and better generalization of the learned models to unseen instances, and it enables more efficient recognition. With this goal in mind, we have designed a representation and recognition framework that captures structural variability and shared part structure within and among object classes. The framework uses probabilistic geometric grammars (PGGs) to represent object classes recursively in terms of their parts, thereby exploiting the hierarchical and substitutive structure inherent to many types of objects. To incorporate geometric and appearance information, we extend traditional probabilistic context-free grammars to represent distributions over the relative geometric characteristics of object parts as well as the appearance of primitive parts. We describe an efficient dynamic programming algorithm for object categorization and localization in images given a PGG model. We also develop an EM algorithm to estimate the parameters of a grammar structure from training data, and a search-based structure learning approach that finds a compact grammar to explain the image data while sharing substructure among classes. Finally, we describe a set of experiments that demonstrate empirically that the system provides a performance benefit.