Advances in Unmanned Aerial Vehicles (UAVs), also known as drones, offer unprecedented opportunities to boost a wide array of large-scale Internet of Things (IoT) applications. Nevertheless, UAV platforms still face important limitations mainly related to autonomy and weight that impact their remote sensing capabilities when capturing and processing the data required for developing autonomous and robust real-time obstacle detection and avoidance systems. In this regard, Deep Learning (DL) techniques have arisen as a promising alternative for improving real-time obstacle detection and collision avoidance for highly autonomous UAVs. This article reviews the most recent developments on DL Unmanned Aerial Systems (UASs) and provides a detailed explanation on the main DL techniques. Moreover, the latest DL-UAV communication architectures are studied and their most common hardware is analyzed. Furthermore, this article enumerates the most relevant open challenges for current DL-UAV solutions, thus allowing future researchers to define a roadmap for devising the new generation affordable autonomous DL-UAV IoT solutions.