This paper addresses the problem of local 3D surface description for surface matching tasks, such as 3D object recognition and surface alignment. The authors categorize existing methods into two main classes: *Signatures* and *Histograms*. They highlight the key issues of uniqueness and repeatability of the local reference frame (RF) in Signature-based methods and propose a novel comprehensive approach that combines the strengths of both classes. The proposed method includes a new unique and repeatable local RF and a 3D descriptor called Signature of Histograms of Orientations (SHOT). SHOT encodes histograms of first-order differential entities (e.g., normals) within a local support, leveraging the robustness of histograms and the descriptive power of signatures. The authors conduct experiments on publicly available datasets and range scans obtained with Spacetime Stereo, demonstrating the effectiveness of their proposal in terms of robustness, descriptiveness, and computational efficiency. The results show that SHOT outperforms state-of-the-art methods in various scenarios, including noise robustness, point density variation, and real-world applications such as 3D reconstruction from Spacetime Stereo data.This paper addresses the problem of local 3D surface description for surface matching tasks, such as 3D object recognition and surface alignment. The authors categorize existing methods into two main classes: *Signatures* and *Histograms*. They highlight the key issues of uniqueness and repeatability of the local reference frame (RF) in Signature-based methods and propose a novel comprehensive approach that combines the strengths of both classes. The proposed method includes a new unique and repeatable local RF and a 3D descriptor called Signature of Histograms of Orientations (SHOT). SHOT encodes histograms of first-order differential entities (e.g., normals) within a local support, leveraging the robustness of histograms and the descriptive power of signatures. The authors conduct experiments on publicly available datasets and range scans obtained with Spacetime Stereo, demonstrating the effectiveness of their proposal in terms of robustness, descriptiveness, and computational efficiency. The results show that SHOT outperforms state-of-the-art methods in various scenarios, including noise robustness, point density variation, and real-world applications such as 3D reconstruction from Spacetime Stereo data.