Body mass index (BMI) exhibits a U-shaped relation to all-cause mortality. The excess mortality associated with obesity is attributable mainly to vascular mortality, but many other diseases also contribute. Increased incidence of disease, rather than increased case fatality, drives excess mortality. The BMI associated with the lowest mortality (nadir) is in the interval of 20-25 kg/m2 but may increase above 25 kg/m2 with advancing age. Instrumental variable analyses indicate that the higher mortality above the nadir is causal. The effect of obesity on mortality is weaker in women than in men and in older than in younger adults. Various cofactors mediate and moderate the effects of obesity on mortality. The U-shaped relation of BMI to mortality is a composite effect of declining mortality by greater fat-free body mass and higher mortality by greater body fat mass. Relative excess fat mass in the abdominal and, especially, visceral area exacerbates the association with mortality, whereas relative excess fat mass in peripheral body regions is not associated with increased mortality. Reducing body weight may reduce mortality when obesity is severe or associated with elevated risk factors or comorbidities, but counteracting effects, possibly on fat-free body mass, may limit the reductions in mortality with weight loss.