Recently, various advanced 3D scanners have been widely used in manufacturing industries to collect 3D point cloud data of fabricated artifacts. The extra dimension of 3D point cloud data can provide more detailed descriptions of anomalies in artifact surfaces than 2D image data. 3D point cloud data can be categorized into structured and unstructured point clouds. Compared with structured 3D point cloud data, unstructured point cloud data can capture the surface geometry more completely. However, anomaly detection and classification by using unstructured 3D point cloud data is more challenging due to unstructured data representation, inconsistent point sizes, and high dimensionality. To deal with these challenges, this talk will present some recent advances in anomaly detection and classification by using unstructured 3D point cloud data. The accuracy and robustness of the proposed method are validated by simulation studies and case studies.