The increase in survival of the very low birth weight baby has meant a challenge for the medical team involved in the care of the very low birth weight infant, in terms of its nutritional requirements, and to achieve the final objective of an optimal growth and development while hospitalized. The objective of this article is to summarize the actual knowledge of the nutritional requirements, the clinical practice, and the scientific principles utilized in the nutrition of these babies. We discuss the recommendations with respect to caloric needs, especific nutritional support and hidration needs, along with the different feeding strategies, offering practical recommendations to achieve an optimal nutrition. Furthermore we present the clinical practice and strategies of feeding which modify the risk of necrotizing enterocolitis, offering recommendations to avoid this feared surgical complication. Existing scientific evidence highlights the importance of supplementing the premature infant with sufficient nutrients, not only to improve survival, growth and neurological development, but also in its future health and quality of life. We evaluate the benefits and risks of different clinical practices, emphasing those with sufficient scientific evidence to be an integral part of the premature nutrition, in terms of early parenteral support of proteins and calories, minimal enteral feeding with maternal milk and the use of fortified formulas and to actively promove maternal lactancia.