Recent years have seen an unprecedented spread of Unmanned Aerial Vehicles (UAVs, or “drones”), which are highly useful for both civilian and military applications. Flight safety is a crucial issue in UAV navigation, having to ensure accurate compliance with recently legislated rules and regulations. The emerging use of autonomous drones and UAV swarms raises additional issues, making it necessary to transfuse safety- and regulations-awareness to relevant algorithms and architectures. Computer vision plays a pivotal role in such autonomous functionalities. Although the main aspects of autonomous UAV technologies (e.g., path planning, navigation control, landing control, mapping and localization, target detection/tracking) are already mature and well-covered, ensuring safe flying in the vicinity of crowds, avoidance of passing over persons, or guaranteed emergency landing capabilities in case of malfunctions, are generally treated as an afterthought when designing autonomous UAV platforms for unstructured environments. This fact is reflected in the fragmentary coverage of the above issues in current literature. This overview attempts to remedy this situation, from the point of view of computer vision. It examines the field from multiple aspects, including regulations across the world and relevant current technologies. Finally, since very few attempts have been made so far towards a complete UAV safety flight and landing pipeline, an example computer vision-based UAV flight safety pipeline is introduced, taking into account all issues present in current autonomous drones. The content is relevant to any kind of autonomous drone flight (e.g., for movie/TV production, news-gathering, search and rescue, surveillance, inspection, mapping, wildlife monitoring, crowd monitoring/management), making this a topic of broad interest.