Modern camera localization methods that use image retrieval, feature matching, and 3D structure-based pose estimation require long-term storage of numerous scene images or a vast amount of image features. This can make them unsuitable for resource constrained VR/AR devices and also raises serious privacy concerns. We present a new learned camera localization technique that eliminates the need to store features or a detailed 3D point cloud. Our key idea is to implicitly encode the appearance of a sparse yet salient set of 3D scene points into a convolutional neural network (CNN) that can detect these scene points in query images whenever they are visible. We refer to these points as scene landmarks. We also show that a CNN can be trained to regress bearing vectors for such landmarks even when they are not within the camera's field-of-view. We demonstrate that the predicted landmarks yield accurate pose estimates and that our method outperforms DSAC*, the state-of-the-art in learned localization. Furthermore, extending HLoc (an accurate method) by combining its correspondences with our predictions, boosts its accuracy even further.