Bangladesh, the eighth most populous country in the world with about 153 million people, has recently been applauded as an exceptional health performer. In the first paper in this Series, we present evidence to show that Bangladesh has achieved substantial health advances, but the country's success cannot be captured simplistically because health in Bangladesh has the paradox of steep and sustained reductions in birth rate and mortality alongside continued burdens of morbidity. Exceptional performance might be attributed to a pluralistic health system that has many stakeholders pursuing women-centred, gender-equity-oriented, highly focused health programmes in family planning, immunisation, oral rehydration therapy, maternal and child health, tuberculosis, vitamin A supplementation, and other activities, through the work of widely deployed community health workers reaching all households. Government and non-governmental organisations have pioneered many innovations that have been scaled up nationally. However, these remarkable achievements in equity and coverage are counterbalanced by the persistence of child and maternal malnutrition and the low use of maternity-related services. The Bangladesh paradox shows the net outcome of successful direct health action in both positive and negative social determinants of health--ie, positives such as women's empowerment, widespread education, and mitigation of the effect of natural disasters; and negatives such as low gross domestic product, pervasive poverty, and the persistence of income inequality. Bangladesh offers lessons such as how gender equity can improve health outcomes, how health innovations can be scaled up, and how direct health interventions can partly overcome socioeconomic constraints.