Deep neural networks on 3D point cloud data have been widely used in the real world, especially in safety-critical applications. However, their robustness against corruptions is less studied. In this paper, we present ModelNet40-C, the first comprehensive benchmark on 3D point cloud corruption robustness, consisting of 15 common and realistic corruptions. Our evaluation shows a significant gap between the performances on ModelNet40 and ModelNet40-C for state-of-the-art (SOTA) models. To reduce the gap, we propose a simple but effective method by combining PointCutMix-R and TENT after evaluating a wide range of augmentation and testtime adaptation strategies. We identify a number of critical insights for future studies on corruption robustness in point cloud recognition. For instance, we unveil that Transformer-based architectures with proper training recipes achieve the strongest robustness. We hope our in-depth analysis will motivate the development of robust training strategies or architecture designs in the 3D point cloud domain. Our codebase and dataset are included in https://github. com/jiachens/ModelNet40-C.