© 2015, Springer Science+Business Media New York. A number of 3D local feature descriptors have been proposed in the literature. It is however, unclear which descriptors are more appropriate for a particular application. A good descriptor should be descriptive, compact, and robust to a set of nuisances. This paper compares ten popular local feature descriptors in the contexts of 3D object recognition, 3D shape retrieval, and 3D modeling. We first evaluate the descriptiveness of these descriptors on eight popular datasets which were acquired using different techniques. We then analyze their compactness using the recall of feature matching per each float value in the descriptor. We also test the robustness of the selected descriptors with respect to support radius variations, Gaussian noise, shot noise, varying mesh resolution, distance to the mesh boundary, keypoint localization error, occlusion, clutter, and dataset size. Moreover, we present the performance results of these descriptors when combined with different 3D keypoint detection methods. We finally analyze the computational efficiency for generating each descriptor.