Recently, text-guided 3D generative methods have made remarkable advancements in producing high-quality textures and geometry, capitalizing on the proliferation of large vision-language and image diffusion models. However, existing methods still struggle to create high-fidelity 3D head avatars in two aspects: (1) They rely mostly on a pre-trained text-to-image diffusion model whilst missing the necessary 3D awareness and head priors. This makes them prone to inconsistency and geometric distortions in the generated avatars. (2) They fall short in fine-grained editing. This is primarily due to the inherited limitations from the pre-trained 2D image diffusion models, which become more pronounced when it comes to 3D head avatars. In this work, we address these challenges by introducing a versatile coarse-to-fine pipeline dubbed HeadSculpt for crafting (i.e., generating and editing) 3D head avatars from textual prompts. Specifically, we first equip the diffusion model with 3D awareness by leveraging landmark-based control and a learned textual embedding representing the back view appearance of heads, enabling 3D-consistent head avatar generations. We further propose a novel identity-aware editing score distillation strategy to optimize a textured mesh with a high-resolution differentiable rendering technique. This enables identity preservation while following the editing instruction.We showcase HeadSculpt's superior fidelity and editing capabilities through comprehensive experiments and comparisons with existing methods.