For decades, researchers have been puzzled by the finding that despite low socioeconomic status, fewer social mobility opportunities, and access barriers to health care, some migrant groups appear to experience lower mortality than the majority population of the respective host country (and possibly also of the country of origin). This phenomenon has been acknowledged as a paradox, and in turn, researchers attempted to explain this paradox through theoretical interpretations, innovative research designs, and methodological speculations. Specific focus on the salmon effect/bias and the convergence theory may help characterize the past and current tendencies in migrant health research to explain the paradox of healthy migrants: the first examines whether the paradox reveals a real effect or is a reflection of methodological error, and the second suggests that even if migrants indeed have a mortality advantage, it may soon disappear due to acculturation. These discussions should encompass mental health in addition to physical health. It is impossible to forecast the future trajectories of migration patterns and equally impossible to always accurately predict the physical and mental health outcomes migrants/refugees who cannot return to the country of origin in times of war, political conflict, and severe climate change. However, following individuals on their path to becoming acculturated to new societies will not only enrich our understanding of the relationship between migration and health but also contribute to the acculturation process by generating advocacy for inclusive health care.