Objective The goal of nutrition of the preterm infant is to meet the growth rate of the healthy fetus of the same gestational age and to produce the same body composition of the healthy fetus in terms of organ growth, tissue components, and cell number and structure. Nutritional quantity and quality are fundamental for normal growth and development of preterm infants, including neurodevelopmental outcomes. Failure to provide the necessary amounts of all of the essential nutrients has produced not only growth failure, but also increased morbidity and less than optimal neurodevelopment. Growth velocities during the NICU hospitalization period for preterm infants exert a significant effect on neurodevelopmental and anthropometric outcomes. Despite the obvious need for optimal nutrition, growth failure is almost universal among preterm infants. There is every reason, therefore, to optimize nutrition of the preterm infant, in terms of total energy and protein, but also in terms of individual components such as amino acids, specific carbohydrates and lipids, and even oxygen. This review presents scientific rationale for nutrient requirements and practical guidelines and approaches to intravenous and enteral feeding for preterm infants. Intravenous feeding, including amino acids, should be started right after birth at rates that are appropriate for the gestational age of the infant. Enteral feeding should be started as soon as possible after birth, using mother's colostrum and milk as first choices. Enteral feeding should begin with trophic amounts and advanced as rapidly as tolerated, decreasing IV nutrition accordingly, while maintaining nutrient intakes at recommended rates. Feeding protocols are valuable for improving nutrition and related outcomes. Further research is needed to determine the optimal nutrition and rate of growth in preterm infants that will achieve optimal neurocognitive benefits while minimizing the longer-term risk of chronic diseases.