Wire arc additive manufacturing (WAAM) offers a level of geometric flexibility and automation that has yet to be seen in construction, and brings new opportunities to optimise material use in structures and reduce embodied carbon. Despite the advantages of AM, the relatively low productivity and high cost are a major barrier to its wider application in construction. In this context, a form of hybrid construction, in which conventional structural elements are coupled with WAAM, has emerged and is the focus of the present paper. The concept is to utilise the efficiency of established manufacturing methods such as hot-rolling or cold-forming to produce the bulk of a structure, but to exploit the geometric freedom of WAAM to make targeted additions that bring about disproportionate benefits. These benefits could be in terms of improved structural performance and efficiency, material savings, weight reductions, reductions in environmental impact, increased automation or reduced costs. By limiting printing only to the parts that require the geometric flexibility offered by WAAM, hybrid construction increases the viability of using this technology in practice. A review of applications of the hybrid construction concept is presented, covering a range of scenarios including the strengthening of structural members, the addition of structural details, the creation of joints, the repair of damaged elements and the facilitation of reuse. The importance of structural optimisation is highlighted, the effects of thermally-induced residual stresses and deformations are discussed and the implications on carbon emissions are explored. Finally, an outlook for the industrialisation of the described form of hybrid construction featuring WAAM, including the key challenges and opportunities in terms of sustainability, economic viability, printability, multi-material and on-site construction applications and structural design, is set out.