In this paper, we propose 3D point-capsule networks, an auto-encoder designedto process sparse 3D point clouds while preserving spatial arrangements of theinput data. 3D capsule networks arise as a direct consequence of our novelunified 3D auto-encoder formulation. Their dynamic routing scheme and thepeculiar 2D latent space deployed by our approach bring in improvements forseveral common point cloud-related tasks, such as object classification, objectreconstruction and part segmentation as substantiated by our extensiveevaluations. Moreover, it enables new applications such as part interpolationand replacement.