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While 6D object pose estimation has recently made a huge leap forward, most methods can still only handle a single or a handful of different objects, which limits their applications. To circumvent this problem, category-level object pose estimation has recently been revamped, which aims at predicting the 6D pose as well as the 3D metric size for previously unseen instances from a given set of object classes. This is, however, a much more challenging task due to severe intra-class shape variations. To address this issue, we propose GPV-Pose, a novel framework for robust category-level pose estimation, harnessing geometric insights to enhance the learning of category-level pose-sensitive features. First, we introduce a decoupled confidence-driven rotation representation, which allows geometry-aware recovery of the associated rotation matrix. Second, we propose a novel geometry-guided point-wise voting paradigm for robust retrieval of the 3D object bounding box. Finally, leveraging these different output streams, we can enforce several geometric consistency terms, further increasing performance, especially for non-symmetric categories. GPV-Pose produces superior results to state-of-the-art competitors on common public benchmarks, whilst almost achieving real-time inference speed at 20 FPS.