The rapid emergence of airborne platforms and imaging sensors are enabling new forms of aerial surveillance due to their unprecedented advantages in scale, mobility, deployment and covert observation capabilities. This paper provides a comprehensive overview of human-centric aerial surveillance tasks from a computer vision and pattern recognition perspective. It aims to provide readers with an in-depth systematic review and technical analysis of the current state of aerial surveillance tasks using drones, UAVs and other airborne platforms. The main object of interest is humans, where single or multiple subjects are to be detected, identified, tracked, re-identified and have their behavior analyzed. More specifically, for each of these four tasks, we first discuss unique challenges in performing these tasks in an aerial setting compared to a ground-based setting. We then review and analyze the aerial datasets publicly available for each task, and delve deep into the approaches in the aerial literature and investigate how they presently address the aerial challenges. We conclude the paper with discussion on the missing gaps and open research questions to inform future research avenues.