Lighting is a critical element of portrait photography. However, good lighting design typically requires complex equipment and significant time and expertise. Our work simplifies this task using a relighting technique that transfers the desired illumination of one portrait onto another. The novelty in our approach to this challenging problem is our formulation of relighting as a mass transport problem. We start from standard color histogram matching that only captures the overall tone of the illumination, and we show how to use the mass-transport formulation to make it dependent on facial geometry. We fit a three-dimensional (3D) morphable face model to the portrait, and for each pixel, we combine the color value with the corresponding 3D position and normal. We then solve a mass-transport problem in this augmented space to generate a color remapping that achieves localized, geometry-aware relighting. Our technique is robust to variations in facial appearance and small errors in face reconstruction. As we demonstrate, this allows our technique to handle a variety of portraits and illumination conditions, including scenarios that are challenging for previous methods.