3D face recognition has become a trending research direction in both industry and academia. It inherits advantages from traditional 2D face recognition, such as the natural recognition process and a wide range of applications. Moreover, 3D face recognition systems could accurately recognize human faces even under dim lights and with variant facial positions and expressions, in such conditions 2D face recognition systems would have immense difficulty to operate. This paper summarizes the history and the most recent progresses in 3D face recognition research domain. The frontier research results are introduced in three categories: pose-invariant recognition, expression-invariant recognition, and occlusion-invariant recognition. To promote future research, this paper collects information about publicly available 3D face databases. This paper also lists important open problems.