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A 3D landmark detection method for 3D facial scans is presented and thoroughly evaluated. The main contribution of the presented method is the automatic and pose-invariant detection of landmarks on 3D facial scans under large yaw variations (that often result in missing facial data), and its robustness against large facial expressions. Three-dimensional information is exploited by using 3D local shape descriptors to extract candidate landmark points. The shape descriptors include the shape index, a continuous map of principal curvature values of a 3D object's surface, and spin images, local descriptors of the object's 3D point distribution. The candidate landmarks are identified and labeled by matching them with a Facial Landmark Model (FLM) of facial anatomical landmarks. The presented method is extensively evaluated against a variety of 3D facial databases and achieves state-of-the-art accuracy (4.5-6.3 mm mean landmark localization error), considerably outperforming previous methods, even when tested with the most challenging data.