We introduce a neural relighting algorithm for captured indoors scenes, that allows interactive free-viewpoint navigation. Our method allows illumination to be changed synthetically, while coherently rendering cast shadows and complex glossy materials. We start with multiple images of the scene and a three-dimensional mesh obtained by multi-view stereo (MVS) reconstruction. We assume that lighting is well explained as the sum of a view-independent diffuse component and a view-dependent glossy term concentrated around the mirror reflection direction. We design a convolutional network around input feature maps that facilitate learning of an implicit representation of scene materials and illumination, enabling both relighting and free-viewpoint navigation. We generate these input maps by exploiting the best elements of both image-based and physically based rendering. We sample the input views to estimate diffuse scene irradiance, and compute the new illumination caused by user-specified light sources using path tracing. To facilitate the network's understanding of materials and synthesize plausible glossy reflections, we reproject the views and compute mirror images . We train the network on a synthetic dataset where each scene is also reconstructed with MVS. We show results of our algorithm relighting real indoor scenes and performing free-viewpoint navigation with complex and realistic glossy reflections, which so far remained out of reach for view-synthesis techniques.