The importance of progressive collapse analysis of structures has increased significantly due to various structural collapses. Single-layer lattice shell structures are susceptible to progressive collapse, as the failure or instability of a localised region can result in a global collapse due to their lightness and wide span. The geometry of these structures plays a crucial role in the load resistance, and any damage that alters the overall geometry can initiate different instabilities, which may also result in progressive collapse. Therefore, the possibility of progressive collapse is high among these lighter structural forms. However, research on the progressive collapse of single-layer lattice shell structures is limited compared to framed structures, highlighting the need for further investigation. Therefore, this manuscript aims to provide a comprehensive review of research conducted on the progressive collapse of single-layer lattice shell structures, focusing on experimental, numerical, and theoretical investigations. Earlier studies have explored the propagation of local instabilities leading to overall failure. More recent research has primarily focused on two approaches: (1) alternate path analysis, which examines the structure’s response after removing a member, and (2) substructure analysis, which aims to identify collapse-preventive mechanisms. Based on these analyses, various methods to enhance progressive collapse resistance have been discussed, including specific local resistance, alternate load paths, compartmentalisation, and tie forces. This review also highlights the limitations present in the current literature and suggests future research directions, which helps to develop design guidelines that can effectively increase the progressive collapse resistance of single-layer lattice shell structures, making them more reliable for various structural applications.