Local shape description is an essential component for many 3D computer vision and graphics applications. This chapter focuses on local descriptors, which, in contrast to global descriptors, encode the shape of small patches around a set of specific keypoints. It presents the challenges and requirements for the design of a 3D keypoint detector and a feature descriptor. The chapter introduces the basic concepts, the taxonomy, and several representative methods for 3D keypoint detection and feature description. It discusses a few fundamental techniques, which have been used to aggregate local descriptors into global descriptors, which in turn can be used for 3D shape retrieval and classification tasks. In general, a local descriptor captures only a few information about a 3D object because of its local support. The chapter describes one popular technique, called the bag of features (BoF), which originated from the text analysis community but has been widely adopted in image and 3D shape analysis.