A novel learnable line segment detector and descriptor is proposed which allows efficient extraction and matching of 2D lines via the angular distance of 128 dimensional unit descriptor vectors. While many handcrafted and deep features have been proposed for keypoints, only a few methods exist for line segments. It is well known, however, that line segments are commonly found in man-made environments, in particular urban scenes, thus they are important for applications like pose estimation, visual odometry, or 3D reconstruction. Our method relies on a 2-stage deep convolutional neural network architecture: In stage 1, candidate 2D line segments are detected, and in stage 2, a descriptor is generated for the extracted lines. The network is trained in a self-supervised way using an automatically collected dataset of matching and non-matching line segments across (substantially) different views of 3D lines. Experimental results confirm the state of the art performance of the proposed L2D2 network on two well-known datasets for autonomous driving both in terms of detected line matches as well as when used for line-based camera pose estimation and tracking.