Background Underweight, overweight, and obesity in childhood and adolescence are associated with adverse health consequences throughout the life-course. Our aim was to estimate worldwide trends in mean body-mass index (BMI) and a comprehensive set of BMI categories that cover underweight to obesity in children and adolescents, and to compare trends with those of adults. Methods We pooled 2416 population-based studies with measurements of height and weight on 128·9 million participants aged 5 years and older, including 31·5 million aged 5–19 years. We used a Bayesian hierarchical model to estimate trends from 1975 to 2016 in 200 countries for mean BMI and for prevalence of BMI in the following categories for children and adolescents aged 5–19 years: more than 2 SD below the median of the WHO growth reference for children and adolescents (referred to as moderate and severe underweight hereafter), 2 SD to more than 1 SD below the median (mild underweight), 1 SD below the median to 1 SD above the median (healthy weight), more than 1 SD to 2 SD above the median (overweight but not obese), and more than 2 SD above the median (obesity). Findings Regional change in age-standardised mean BMI in girls from 1975 to 2016 ranged from virtually no change (−0·01 kg/m2 per decade; 95% credible interval −0·42 to 0·39, posterior probability [PP] of the observed decrease being a true decrease=0·5098) in eastern Europe to an increase of 1·00 kg/m2 per decade (0·69–1·35, PP>0·9999) in central Latin America and an increase of 0·95 kg/m2 per decade (0·64–1·25, PP>0·9999) in Polynesia and Micronesia. The range for boys was from a non-significant increase of 0·09 kg/m2 per decade (−0·33 to 0·49, PP=0·6926) in eastern Europe to an increase of 0·77 kg/m2 per decade (0·50–1·06, PP>0·9999) in Polynesia and Micronesia. Trends in mean BMI have recently flattened in northwestern Europe and the high-income English-speaking and Asia-Pacific regions for both sexes, southwestern Europe for boys, and central and Andean Latin America for girls. By contrast, the rise in BMI has accelerated in east and south Asia for both sexes, and southeast Asia for boys. Global age-standardised prevalence of obesity increased from 0·7% (0·4–1·2) in 1975 to 5·6% (4·8–6·5) in 2016 in girls, and from 0·9% (0·5–1·3) in 1975 to 7·8% (6·7–9·1) in 2016 in boys; the prevalence of moderate and severe underweight decreased from 9·2% (6·0–12·9) in 1975 to 8·4% (6·8–10·1) in 2016 in girls and from 14·8% (10·4–19·5) in 1975 to 12·4% (10·3–14·5) in 2016 in boys. Prevalence of moderate and severe underweight was highest in India, at 22·7% (16·7–29·6) among girls and 30·7% (23·5–38·0) among boys. Prevalence of obesity was more than 30% in girls in Nauru, the Cook Islands, and Palau; and boys in the Cook Islands, Nauru, Palau, Niue, and American Samoa in 2016. Prevalence of obesity was about 20% or more in several countries in Polynesia and Micronesia, the Middle East and north Africa, the Caribbean, and the USA. In 2016, 75 (44–117) million girls and 117 (70–178) million boys worldwide were moderately or severely underweight. In the same year, 50 (24–89) million girls and 74 (39–125) million boys worldwide were obese. Interpretation The rising trends in children's and adolescents' BMI have plateaued in many high-income countries, albeit at high levels, but have accelerated in parts of Asia, with trends no longer correlated with those of adults. Funding Wellcome Trust, AstraZeneca Young Health Programme.