We propose DenseMarks - a new learned representation for human heads, enabling high-quality dense correspondences of human head images. For a 2D image of a human head, a Vision Transformer network predicts a 3D embedding for each pixel, which corresponds to a location in a 3D canonical unit cube. In order to train our network, we collect a dataset of pairwise point matches, estimated by a state-of-the-art point tracker over a collection of diverse in-the-wild talking heads videos, and guide the mapping via a contrastive loss, encouraging matched points to have close embeddings. We further employ multi-task learning with face landmarks and segmentation constraints, as well as imposing spatial continuity of embeddings through latent cube features, which results in an interpretable and queryable canonical space. The representation can be used for finding common semantic parts, face/head tracking, and stereo reconstruction. Due to the strong supervision, our method is robust to pose variations and covers the entire head, including hair. Additionally, the canonical space bottleneck makes sure the obtained representations are consistent across diverse poses and individuals. We demonstrate state-of-the-art results in geometry-aware point matching and monocular head tracking with 3D Morphable Models. The code and the model checkpoint will be made available to the public.