Metal additive manufacturing is gaining immense research attention. Some of these research efforts are associated with physics, statistical, or artificial intelligence-driven process modelling and optimisation, structure–property characterisation, structural design optimisation, or equipment enhancements for cost reduction and faster throughputs. In this review, the focus is drawn on the utilisation of topology optimisation for structural design in metal additive manufacturing. First, the symbiotic relationship between topology optimisation and metal additive manufacturing in aerospace, medical, automotive, and other industries is investigated. Second, support structure design by topology optimisation for thermal-based powder-bed processes is discussed. Third, the introduction of capabilities to limit manufacturing constraints and generate porous features in topology optimisation is examined. Fourth, emerging efforts to adopt artificial intelligence models are examined. Finally, some open-source and commercial software with capabilities for topology optimisation and metal additive manufacturing are explored. This study considers the challenges faced while providing perceptions on future research directions.