Nutrition of preterm infants should result in growth similar to that of normally growing fetuses of the same gestational age. Unfortunately, most preterm infants are not fed enough to achieve this objective; as a result they are growth restricted by term gestation. Recent studies have demonstrated that early and enhanced “aggressive” nutrition of preterm infants can reduce postnatal growth failure and improve longer-term outcomes, particularly for the brain and its cognitive functions. When preterm infants are fed more aggressively (earlier onset of intravenous and enteral feeding, earlier achievement of full enteral feeding) cumulative energy and protein deficits are reduced and they consistently regain birth weight sooner, the incidence of necrotizing enterocolitis and late-onset sepsis is unchanged or reduced, and they achieve discharge criteria and go home sooner, with overall shorter hospital stays, and have improved anthropometrics by term gestation. More research is needed, however, to determine optimum feeding of preterm infants, particularly during periods of illness and physiological instability.