Face recognition is a popular research topic with a number of applications in several industrial sectors including security, surveillance, entertainment, virtual reality, and human–machine interaction. Both 2D images and 3D data can now be easily acquired and used for face recognition. For any 2D/3D face recognition system, feature extraction and selection play a significant role. Currently, both holistic and local features have been intensively investigated in the literature. In this article, fundamental background knowledge of face recognition, including 2D/3D data acquisition, data preprocessing, feature extraction, classification, and performance evaluation, is presented. The state‐of‐the‐art feature extraction algorithms, including 2D holistic feature, 2D local feature, 3D holistic feature, and 3D local feature extraction algorithms, are then described in detail. Finally, feature selection and fusion techniques are presented. The article covers the complete related aspects of feature selection for 2D and 3D face recognition.