Civilian drones are soon expected to be used in a wide variety of tasks, such as aerial surveillance, delivery, or monitoring of existing architectures. Nevertheless, their deployment in urban environments has so far been limited. Indeed, in unstructured and highly dynamic scenarios, drones face numerous challenges to navigate autonomously in a feasible and safe way. In contrast to traditional “map-localize-plan” methods, this letter explores a data-driven approach to cope with the above challenges. To accomplish this, we propose DroNet: a convolutional neural network that can safely drive a drone through the streets of a city. Designed as a fast eight-layers residual network, DroNet produces two outputs for each single input image: A steering angle to keep the drone navigating while avoiding obstacles, and a collision probability to let the UAV recognize dangerous situations and promptly react to them. The challenge is however to collect enough data in an unstructured outdoor environment such as a city. Clearly, having an expert pilot providing training trajectories is not an option given the large amount of data required and, above all, the risk that it involves for other vehicles or pedestrians moving in the streets. Therefore, we propose to train a UAV from data collected by cars and bicycles, which, already integrated into the urban environment, would not endanger other vehicles and pedestrians. Although trained on city streets from the viewpoint of urban vehicles, the navigation policy learned by DroNet is highly generalizable. Indeed, it allows a UAV to successfully fly at relative high altitudes and even in indoor environments, such as parking lots and corridors. To share our findings with the robotics community, we publicly release all our datasets, code, and trained networks.