Emerging Metaverse applications demand accessible, accurate and easy-to-use tools for 3D digital human creations in order to depict different cultures and societies as if in the physical world. Recent large-scale vision-language advances pave the way for novices to conveniently customize 3D content. However, the generated CG-friendly assets still cannot represent the desired facial traits for human characteristics. In this paper, we present Dream-Face, a progressive scheme to generate personalized 3D faces under text guidance. It enables layman users to naturally customize 3D facial assets that are compatible with CG pipelines, with desired shapes, textures and fine-grained animation capabilities. From a text input to describe the facial traits, we first introduce a coarse-to-fine scheme to generate the neutral facial geometry with a unified topology. We employ a selection strategy in the CLIP embedding space to generate coarse geometry, and subsequently optimize both the detailed displacements and normals using Score Distillation Sampling (SDS) from the generic Latent Diffusion Model (LDM). Then, for neutral appearance generation, we introduce a dual-path mechanism, which combines the generic LDM with a novel texture LDM to ensure both the diversity and textural specification in the UV space. We also employ a two-stage optimization to perform SDS in both the latent and image spaces to significantly provide compact priors for fine-grained synthesis. It also enables learning the mapping from the compact latent space into physically-based textures (diffuse albedo, specular intensity, normal maps, etc.). Our generated neutral assets naturally support blendshapes-based facial animations, thanks to the unified geometric topology. We further improve the animation ability with personalized deformation characteristics. To this end, we learn the universal expression prior in a latent space with neutral asset conditioning using the cross-identity hypernetwork, we subsequently train a neural facial tracker from video input space into the pre-trained expression space for personalized fine-grained animation. Extensive qualitative and quantitative experiments validate the effectiveness and generalizability of DreamFace. Notably, DreamFace can generate realistic 3D facial assets with physically-based rendering quality and rich animation ability from video footage, even for fashion icons or exotic characters in cartoons and fiction movies.