BACKGROUND: In the absence of a commonly accepted definition, conversion surgery is generally considered as surgical resection with the intent of prolonging survival after non-surgical induction therapy in patients with upfront unresectable disease at diagnosis. Despite the heterogeneity of possible targets, conversion surgery is a quickly evolving concept, with commonalities for upper gastrointestinal (UGI) and hepato-pancreato-biliary (HPB) malignancies. METHODS: A comprehensive narrative review of the most recent and relevant literature was conducted by experts in the field of different UGI and HPB tumours. RESULTS: The increased interest of the surgical scientific community in the concept of conversion surgery can be explained by the continuous improvements in non-surgical therapies aimed at controlling the systemic tumour burden and the local extension of cancer, supported by improvements in surgical outcomes for advanced resections in expert centres. The toolbox of the surgical oncologist seeking conversion in the case of unresectable UGI and HBP tumours is large and includes (but is not limited to) systemic chemotherapy, (chemo)radiation, targeted therapy/immunotherapy, locoregional ablation techniques, intra-arterial therapies, liver hypertrophy induction techniques, treatments of underlying medical conditions, and prehabilitation. CONCLUSIONS: Conversion surgery represents a powerful instrument to prolong the survival of patients with unresectable UGI and HPB malignancies. However, most of the available evidence is of a low level and at very high risk of selection bias. Alongside a profound understanding of (and respect for) the biology of cancer, which remains key to selecting appropriate patients and avoiding non-therapeutic surgeries, a commonly accepted definition is urgently needed to standardize practice, monitor outcomes, and improve the quality of research.