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Occlusion poses a major challenge for person re-identification (ReID). Existing approaches typically rely on outside tools to infer visible body parts, which may be suboptimal in terms of both computational efficiency and ReID accuracy. In particular, they may fail when facing complex occlusions, such as those between pedestrians. Accordingly, in this paper, we propose a novel method named Quality-aware Part Models (QPM) for occlusion-robust ReID. First, we propose to jointly learn part features and predict part quality scores. As no quality annotation is available, we introduce a strategy that automatically assigns low scores to occluded body parts, thereby weakening the impact of occluded body parts on ReID results. Second, based on the predicted part quality scores, we propose a novel identity-aware spatial attention (ISA) module. In this module, a coarse identity-aware feature is utilized to highlight pixels of the target pedestrian, so as to handle the occlusion between pedestrians. Third, we design an adaptive and efficient approach for generating global features from common non-occluded regions with respect to each image pair. This design is crucial, but is often ignored by existing methods. QPM has three key advantages: 1) it does not rely on any outside tools in either the training or inference stages; 2) it handles occlusions caused by both objects and other pedestrians;3) it is highly computationally efficient. Experimental results on four popular databases for occluded ReID demonstrate that QPM consistently outperforms state-of-the-art methods by significant margins. The code of QPM will be released.