Additive manufacturing methods(1-4) using static and mobile robots are being developed for both on-site construction(5-8) and off-site prefabrication(9,10). Here we introduce a method of additive manufacturing, referred to as aerial additive manufacturing (Aerial-AM), that utilizes a team of aerial robots inspired by natural builders(11) such as wasps who use collective building methods(12,13). We present a scalable multi-robot three-dimensional (3D) printing and path-planning framework that enables robot tasks and population size to be adapted to variations in print geometry throughout a building mission. The multi-robot manufacturing framework allows for autonomous three-dimensional printing under human supervision, real-time assessment of printed geometry and robot behavioural adaptation. To validate autonomous Aerial-AM based on the framework, we develop BuilDrones for depositing materials during flight and ScanDrones for measuring the print quality, and integrate a generic real-time model-predictive-control scheme with the Aerial-AM robots. In addition, we integrate a dynamically self-aligning delta manipulator with the BuilDrone to further improve the manufacturing accuracy to five millimetres for printing geometry with precise trajectory requirements, and develop four cementitious-polymeric composite mixtures suitable for continuous material deposition. We demonstrate proof-of-concept prints including a cylinder 2.05 metres high consisting of 72 layers of a rapid-curing insulation foam material and a cylinder 0.18 metres high consisting of 28 layers of structural pseudoplastic cementitious material, a light-trail virtual print of a dome-like geometry, and multi-robot simulations. Aerial-AM allows manufacturing in-flight and offers future possibilities for building in unbounded, at-height or hard-to-access locations.