The fundamental goal of modern medicine is to increase human life expectancy. Currently, most of the patients in hospitals with different clinical profiles are elderly and senile subjects, with a high incidence of comorbidities, as well as concomitant age-related changes in peripheral tissues. One such change is sarcopenia, a progressive loss of muscle mass, strength, and muscle function that is associated with a high risk of adverse outcomes, leading to an increased risk of disability and death among older adults. The mechanisms of development of sarcopenia are currently being actively studied. This narrative review presents the issues of epidemiology, pathophysiology, and diagnostic criteria for sarcopenia. The relationships between sarcopenia and metabolic dysfunction-associated steatotic liver disease (MASLD) with possible promising directions for the treatment of this comorbid pathology are considered.