A common question to many researchers is whether a computer vision system can process and analyze 3D face as the human vision system does. In addition to understanding human cognition, there is also increasing interest in analyzing shapes of facial surfaces for developing applications such as biometrics, humanβcomputer interaction (HCI), facial surgery, video communications, and 3D animation. Contents 1 3D Face Modeling 1.1 Challenges and Taxonomy of Techniques 1.2 Background 1.3 Static 3D Face Modeling 1.4 Dynamic 3D Face Reconstruction 1.5 Summary and Conclusions 2 3D Face Surface Analysis and Recognition Based on Facial Surface Features 2.1 Geometry of 3D Facial Surface 2.2 Curvatures Extraction from 3D Face Surface 2.3 3D Face Segmentation 2.4 3D Face Surface Feature Extraction and Matching 2.5 Deformation Modeling of 3D Face Surface 3 3D Face Surface Analysis and Recognition Based on Facial Curves 3.1 Introduction 3.2 Facial Surface Modeling 3.3 Parametric Representation of Curves 3.4 Facial Shape Representation Using Radial Curves 3.5 Shape Space of Open Curves 3.6 The Dense Scalar Field (DSF) 3.7 Statistical Shape Analysis 3.8 Applications of Statistical Shape Analysis 3.8.2 Hierarchical Organization of Facial Shapes 3.9 The Iso-geodesic Stripes 4 3D Morphable Models for Face Surface Analysis and Recognition 4.1 Introduction 4.2 Data Sets 4.3 Face Model Fitting 4.4 Dynamic Model Expansion 4.5 Face Matching 4.6 Concluding Remarks 5 Applications 5.1 Introduction 5.2 3D Face Databases 5.3 3D Face Recognition 5.4 Facial Expression Analysis 5.5 4D Facial Expression Recognition