3D shape matching refers to the process of determining the amount of similarity between two 3D shapes. A large class of matching methods use feature-based descriptors to determine shape similarity. The use of these descriptors, or feature vectors, enables the 3D matching methods to be applied to a large class of 3D problems such as registration, shape retrieval, shape recognition and classification. In this paper we provide a survey of feature-based approaches to 3D matching, particularly as they apply to global and partial shape matching. Partial shape matching is a more difficult problem than global matching, since the location, size, orientation, or overlap of the 3D models that need to be matched are not known a priori. To alleviate this problem, the majority of partial 3D matching methods use some criteria to pick salient or distinctive points on the models, referred to as feature points. We investigate the different criteria used in selecting these feature points.