As part of a supplement entitled "Born Too Soon", this paper focuses on care of the preterm newborn. An estimated 15 million babies are born preterm, and the survival gap between those born in high and low income countries is widening, with one million deaths a year due to direct complications of preterm birth, and around one million more where preterm birth is a risk factor, especially amongst those who are also growth restricted. Most premature babies (>80%) are between 32 and 37 weeks of gestation, and many die needlessly for lack of simple care. We outline a series of packages of care that build on essential care for every newborn comprising support for immediate and exclusive breastfeeding, thermal care, and hygienic cord and skin care. For babies who do not breathe at birth, rapid neonatal resuscitation is crucial. Extra care for small babies, including Kangaroo Mother Care, and feeding support, can halve mortality in babies weighing <2000 g. Case management of newborns with signs of infection, safe oxygen management and supportive care for those with respiratory complications, and care for those with significant jaundice are all critical, and are especially dependent on competent nursing care. Neonatal intensive care units in high income settings are de-intensifying care, for example increasing use of continuous positive airway pressure (CPAP) and this makes comprehensive preterm care more transferable. For health systems in low and middle income settings with increasing facility births, district hospitals are the key frontier for improving obstetric and neonatal care, and some large scale programmes now include specific newborn care strategies. However there are still around 50 million births outside facilities, hence home visits for mothers and newborns, as well as women's groups are crucial for reaching these families, often the poorest. A fundamental challenge is improving programmatic tracking data for coverage and quality, and measuring disability-free survival. The power of parent's voices has been important in high-income countries in bringing attention to preterm newborns, but is still missing from the most affected countries.