Although still in its infancy, metal additive manufacturing (AM) or 3D printing has now arrived at a scale suitable for use in construction. The new technology offers the potential for improved economy, sustainability, safety and productivity through greater automation, enhanced customisation, reduced material usage and reduced wastage. In this paper, a review of recent developments in metal AM in structural engineering is presented, including the latest research advances, current trends and applications in practice. Emphasis is placed on Directed Energy Deposition-arc (DED-arc) AM or wire arc AM (WAAM) since this is deemed to be the most promising technique for the requirements of the construction sector. A description of the observed material response of both steel and stainless steel WAAM elements, as well as the structural behaviour of cross-sections, members, connections and systems, is provided. The challenges surrounding the inherent geometric variability of as-built WAAM material, as well as the implications of possible anisotropy, are discussed.