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Age estimation and face verification across aging are important problems with a wide range of applications. It is well known that age and identity information are encoded in both texture and shape of the face. Building on recent advances in landmark extraction and statistical techniques for landmark-based shape analysis, we consider these problems using facial shapes. We show that by using well-defined shape spaces and their associated geometry, one can obtain significant performance improvements in both age estimation and face verification. Toward this end, we propose to model the facial shapes as points on a Grassmann manifold. Age estimation and face verification are then considered as regression and classification problems on this manifold. Algorithms for regression and classification are designed to take into account the geometry of the underlying space. The proposed method is flexible and can be used as a standalone age estimator or classifier, and we also present methods for fusion with texture-based algorithms.