This article examines the integration of immersive technologies, including Virtual Reality (VR), Augmented Reality (AR), Extended Reality (XR), Mixed Reality (MR) and the metaverse, in cultural heritage and museums within the context of the green, digital and social sustainability transition. Based on a bibliometric and qualitative analysis of 479 publications and a meta-review of 19 selected studies, the research identifies eight thematic clusters and highlights the uneven integration of environmental and social sustainability alongside digital transformation. The findings also point to the emergence of museums as hybrid innovation spaces connecting technology, territories and community engagement