In this paper we propose to learn a mapping from image pixels into a dense template grid through a fully convolu-tional network. We formulate this task as a regression problem and train our network by leveraging upon manually annotated facial landmarks " in-the-wild ". We use such landmarks to establish a dense correspondence field between a three-dimensional object template and the input image, which then serves as the ground-truth for training our regression system. We show that we can combine ideas from semantic segmentation with regression networks, yielding a highly-accurate 'quantized regression' architecture. Our system, called DenseReg, allows us to estimate dense image-to-template correspondences in a fully convo-lutional manner. As such our network can provide useful correspondence information as a stand-alone system, while when used as an initialization for Statistical Deformable Models we obtain landmark localization results that largely outperform the current state-of-the-art on the challenging 300W benchmark. We thoroughly evaluate our method on a host of facial analysis tasks, and demonstrate its use for other correspondence estimation tasks, such as the human body and the human ear. DenseReg code is made available at http://alpguler.com/DenseReg.html along with supplementary materials.