Knowledge distillation (KD) has witnessed its powerful ability in learning compact models in deep learning field, but it is still limited in distilling localization information for object detection. Existing KD methods for object detection mainly focus on mimicking deep features between teacher model and student model, which not only is restricted by specific model architectures, but also cannot distill localization ambiguity. In this paper, we first propose localization distillation (LD) for object detection. In particular, our LD can be formulated as standard KD by adopting the general localization representation of bounding box. Our LD is very flexible, and is applicable to distill localization ambiguity for arbitrary architecture of teacher model and student model. Moreover, it is interesting to find that Self-LD, i.e., distilling teacher model itself, can further boost state-of-the-art performance. Second, we suggest a teacher assistant (TA) strategy to fill the possible gap between teacher model and student model, by which the distillation effectiveness can be guaranteed even the selected teacher model is not optimal. On benchmark datasets PASCAL VOC and MS COCO, our LD can consistently improve the performance for student detectors, and also boosts state-of-the-art detectors notably. Our source code and trained models are publicly available at https://github.com/HikariTJU/LD