This article is about deep learning (DL) and deep reinforcement learning (DRL) works applied to robotics. Both tools have been shown to be successful in delivering data-driven solutions for robotics tasks, as well as providing a natural way to develop an end-to-end pipeline from the robot’s sensing to its actuation, passing through the generation of a policy to perform the given task. These frameworks have been proven to be able to deal with real-world complications such as noise in sensing, imprecise actuation, variability in the scenarios where the robot is being deployed, among others. Following that vein, and given the growing interest in DL and DRL, the present work starts by providing a brief tutorial on deep reinforcement learning, where the goal is to understand the main concepts and approaches followed in the field. Later, the article describes the main, recent, and most promising approaches of DL and DRL in robotics, with sufficient technical detail to understand the core of the works and to motivate interested readers to initiate their own research in the area. Then, to provide a comparative analysis, we present several taxonomies in which the references can be classified, according to high-level features, the task that the work addresses, the type of system, and the learning techniques used in the work. We conclude by presenting promising research directions in both DL and DRL.