Deep reinforcement learning (RL) has emerged as a promising approach for autonomously acquiring complex behaviors from low level sensor observations. Although a large portion of deep RL research has focused on applications in video games and simulated control, which does not connect with the constraints of learning in real environments, deep RL has also demonstrated promise in enabling physical robots to learn complex skills in the real world. At the same time,real world robotics provides an appealing domain for evaluating such algorithms, as it connects directly to how humans learn; as an embodied agent in the real world. Learning to perceive and move in the real world presents numerous challenges, some of which are easier to address than others, and some of which are often not considered in RL research that focuses only on simulated domains. In this review article, we present a number of case studies involving robotic deep RL. Building off of these case studies, we discuss commonly perceived challenges in deep RL and how they have been addressed in these works. We also provide an overview of other outstanding challenges, many of which are unique to the real-world robotics setting and are not often the focus of mainstream RL research. Our goal is to provide a resource both for roboticists and machine learning researchers who are interested in furthering the progress of deep RL in the real world.