Abstract Background Bangladesh has experienced remarkable transformation in demographic, health, and nutritional status of the population. The changes have exposed the population to a number of challenges, the detrimental effect of which on health and nutrition is likely to be increased by the coronavirus disease 2019 (COVID-19) pandemic. We provide an overview of health and nutritional challenges in Bangladesh in relation to demographic transition and the COVID-19 pandemic. Methods We identified and reviewed recent reports, published articles, and pertinent gray literature on nutrition and food security in Bangladesh to provide historical and contextual information. Results The review identifies the progress as well as existing burden regarding nutrition and food security in Bangladesh and highlights the challenges in the coming days in regard to population growth and the COVID-19 pandemic. The country is on track to reduce all forms of childhood undernutrition, while the proportion of nutrition-related noncommunicable diseases is rising owing to changes in dietary intake, low physical activity, and sedentary lifestyle. Conclusions Despite remarkable progress, health and nutritional status of the population in Bangladesh faces challenges, particularly in relation to demographic transition and compounded by the COVID-19 pandemic, which require concerted attention from policymakers as well as stakeholders.