We present a versatile model, FaceAnime, for various video generation tasks from still images. Video generation from a single face image is an interesting problem and usually tackled by utilizing Generative Adversarial Networks (GANs) to integrate information from the input face image and a sequence of sparse facial landmarks. However, the generated face images usually suffer from quality loss, image distortion, identity change, and expression mismatching due to the weak representation capacity of the facial landmarks. In this paper, we propose to "imagine" a face video from a single face image according to the reconstructed 3D face dynamics, aiming to generate a realistic and identity-preserving face video, with precisely predicted pose and facial expression. The 3D dynamics reveal changes of the facial expression and motion, and can serve as a strong prior knowledge for guiding highly realistic face video generation. In particular, we explore face video prediction and exploit a well-designed 3D dynamic prediction network to predict a 3D dynamic sequence for a single face image. The 3D dynamics are then further rendered by the sparse texture mapping algorithm to recover structural details and sparse textures for generating face frames. Our model is versatile for various AR/VR and entertainment applications, such as face video retargeting and face video prediction. Superior experimental results have well demonstrated its effectiveness in generating high-fidelity, identitypreserving, and visually pleasant face video clips from a single source face image.