Aerial robotics has been one of the most active areas of research within the robotics community, and recently there have been many reports of promising results in aerial swarm systems. This is partly due to the commoditization of multicopter platforms, and communication, sensing, and processing hardware that has substantially lowered the barriers to entry to the field of aerial swarm robotics. Aerial swarms differ from swarms of ground-based vehicles in two major respects: Aerial robots or unmanned aerial vehicles (UAVs) operate in a three-dimensional space, and the dynamics of individual vehicles add an extra layer of complexity to the problems of path planning and trajectory design. Furthermore, the success of aerial swarms is predicated on the distributed and synergistic capabilities of individual and cooperative control, estimation, and decision making of aerial robots with limited resources, such as modest onboard computation and sensing capabilities and size, weight, and power constraints. This special section, starting with the survey paper, presents recent advances in aerial swarm robotics, and aims to put together a cohesive set of research goals and visions toward realizing fully autonomous aerial swarm systems. One objective is to emphasize the three-way tradeoff among computational efficiency for large-scale swarms, stability, and robustness under uncertainty, and the optimal system performance.