Background: Whilst prevention of growth faltering has both short- and long-term health benefits, whether too fast or accelerated infant growth adversely affects later health outcomes is controversial and a major focus of research. Summary: Many observational studies suggest that rapid weight gain in infancy (upward centile crossing) increases the long-term risk of obesity and non-communicable disease. This association has been seen in infants from low- and high-income countries, in infants born preterm or at term, and those born with normal or low birth weight for gestation. Experimental (randomized) studies in both breast- and formula-fed infants support a causal link between early growth acceleration and infant nutrition and later risk of obesity. These observations suggest that strategies to optimize the pattern of infant growth could make a major contribution to stemming the current global epidemic of non-communicable disease. Key Messages: The optimal pattern of infant weight gain is likely to differ in different populations. The benefits of rapid infant weight gain for later neurodevelopment favors the promotion of rapid growth in infants born preterm. However, growth acceleration in healthy infants born at term (either normal or low birth weight for gestation) is likely to have adverse effects for long-term health.