Clinically effective pharmacological treatment(s) for metabolic dysfunction-associated steatotic liver disease (MASLD) and its progressive form metabolic dysfunction-associated steatohepatitis (MASH) represent a largely unmet need in medicine. Since glucagon-like peptide-1 receptor agonists (GLP-1RAs) have been licensed for the treatment of type 2 diabetes mellitus and obesity, they were one of the first drug classes to be examined in individuals with MASLD/MASH. Successful phase 2 randomised clinical trials with these agents have resulted in progression to phase 3 clinical trials (principally testing the long-term efficacy of subcutaneous semaglutide). Over the last few years, in addition to GLP-1RAs, newer agents with glucose-dependent insulinotropic peptide and/or glucagon receptor agonist functions have been tested, with increasing evidence from phase 2 randomised clinical trials of histological improvements in MASLD/MASH, as well as benefits on MASLD-related extrahepatic complications. Based on this background of evidence, single, dual or triple incretin receptor agonists are becoming an attractive and promising treatment option for MASLD or MASH, particularly in individuals with coexisting obesity or type 2 diabetes mellitus. In this narrative review, we examine the rapidly expanding body of clinical evidence supporting a role of incretin-based pharmacotherapies in delaying or reversing MASH progression. We also discuss the biology of incretins and the putative hepatoprotective mechanisms of incretin-based pharmacotherapies for managing MASLD or MASH.