In this paper, we present a framework for detecting interest points in 3-D meshes and computing their corresponding descriptors. For that, we propose an intrinsic scale detection scheme per interest point and utilize it to derive two scale-invariant local features for mesh models. First, we present the scale-invariant spin image local descriptor that is a scale-invariant formulation of the spin image descriptor. Second, we adapt the scale-invariant feature transform feature to mesh data by representing the vicinity of each interest point as a depth map and estimating its dominant angle using the principal component analysis to achieve rotation invariance. The proposed features were experimentally shown to be robust to scale changes and partial mesh matching, and they were compared favorably with other local mesh features on the SHREC'10 and SHREC'11 testbeds. We applied the proposed local features to mesh retrieval using the bag-of-features approach and achieved state-of-the-art retrieval accuracy. Last, we applied the proposed local features to register models to scanned depth scenes and achieved high registration accuracy.