Semantic understanding of 3D objects is crucial in many applications such as object manipulation. However, it is hard to give a universal definition of point-level semantics that everyone would agree on. We observe that people have a consensus on semantic correspondences between two areas from different objects, but are less certain about the exact semantic meaning of each area. Therefore, we argue that by providing human labeled correspondences between different objects from the same category instead of explicit semantic labels, one can recover rich semantic information of an object. In this paper, we introduce a new dataset named CorresPondenceNet. Based on this dataset, we are able to learn dense semantic embeddings with a novel geodesic consistency loss. Accordingly, several state-of-the-art networks are evaluated on this correspondence benchmark. We further show that CorresPondenceNet could not only boost fine-grained understanding of heterogeneous objects but also cross-object registration and partial object matching.