3D single object tracking in LiDAR point clouds (LiDAR SOT) plays a crucial role in autonomous driving. Current approaches all follow the Siamese paradigm based on appearance matching. However, LiDAR point clouds are usually textureless and incomplete, which hinders effective appearance matching. Besides, previous methods greatly overlook the critical motion clues among targets. In this work, beyond 3D Siamese tracking, we introduce a motion-centric paradigm to handle LiDAR SOT from a new perspective. Following this paradigm, we propose a matching-free two-stage tracker M 2 -Track. At the 1 st -stage, M 2 -Track localizes the target within successive frames via motion transformation. Then it refines the target box through motion-assisted shape completion at the 2 nd -stage. Due to the motion-centric nature, our method shows its impressive generalizability with limited training labels and provides good differentiability for end-to-end cycle training. This inspires us to explore semi-supervised LiDAR SOT by incorporating a pseudo-label-based motion augmentation and a self-supervised loss term. Under the fully-supervised setting, extensive experiments confirm that M 2 -Track significantly outperforms previous state-of-the-arts on three large-scale datasets while running at 57FPS (∼ 8%, ∼ 17% and ∼ 22% precision gains on KITTI, NuScenes, and Waymo Open Dataset respectively). While under the semi-supervised setting, our method performs on par with or even surpasses its fully-supervised counterpart using fewer than half labels from KITTI. Further analysis verifies each component's effectiveness and shows the motion-centric paradigm's promising potential for auto-labeling and unsupervised domain adaptation. The code is available at https://github.com/Ghostish/Open3DSOT.