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The construction industry has recently increased the adoption of additive manufacturing (AM, also known as 3D-printing) technologies. This review paper presents the state of the art of ground-based AM systems in construction, focusing comprehensively on developments in the material aspect towards using unmanned aerial vehicles (UAV), commonly referred to as “drones”. AM itself is introduced, and an overview of the history of AM is provided. Key projects developing both ground-based cementitious and polymeric AM applications for construction purposes are reviewed along with material constituents, AM deposition methods and reinforcement techniques to mitigate against crack propagation. The review details a cutting-edge Aerial Additive Manufacturing (AAM) system developed to utilise untethered, self-powered UAV platforms extruding material during autonomous flight, which is designed to bring multi-agent aerial mobility to AM in the construction industry. An overview of the history of UAV development is presented, as well as the current use of UAV platforms combined with material deposition devices for construction and considerations for developing suitable materials and future research.