Recent advancements in large-scale additive manufacturing have extended its application in the building industry, delivering notable gains in productivity, efficiency, environmental sustainability, and safety compared with traditional construction methods. Aerial additive manufacturing (aerial AM), which uses aerial robots for unbounded construction tasks, offers distinct advantages, such as scalability at height, enhanced access to remote or challenging locations, and rapid on-demand repair capabilities. Despite several small-scale demonstrations, deploying aerial robots in construction still presents critical challenges and unresolved scientific questions. This Review provides a comprehensive analysis of current aerial AM research, highlights key opportunities and challenges at large scales, and introduces an autonomy framework aimed at clarifying the overarching challenges inherent in the technology.