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3D object detection is an important yet demanding task that heavily relies on difficult to obtain 3D annotations. To reduce the required amount of supervision, we propose 3DIoUMatch, a novel semi-supervised method for 3D object detection applicable to both indoor and outdoor scenes. We leverage a teacher-student mutual learning framework to propagate information from the labeled to the unlabeled train set in the form of pseudo-labels. However, due to the high task complexity, we observe that the pseudo-labels suffer from significant noise and are thus not directly usable. To that end, we introduce a confidence-based filtering mechanism, inspired by FixMatch. We set confidence thresholds based upon the predicted objectness and class probability to filter low-quality pseudo-labels. While effective, we observe that these two measures do not sufficiently capture localization quality. We therefore propose to use the estimated 3D IoU as a localization metric and set category-aware self-adjusted thresholds to filter poorly localized proposals. We adopt VoteNet as our backbone detector on indoor datasets while we use PV-RCNN on the autonomous driving dataset, KITTI. Our method consistently improves state-of-the-art methods on both ScanNet and SUN-RGBD benchmarks by significant margins under all label ratios (including fully labeled setting). For example, when training using only 10% labeled data on ScanNet, 3DIoUMatch achieves 7.7 absolute improvement on mAP@0.25 and 8.5 absolute improvement on mAP@0.5 upon the prior art. On KITTI, we are the first to demonstrate semi-supervised 3D object detection and our method surpasses a fully supervised baseline from 1.8% to 7.6% under different label ratios and categories.