The choice of palliative care can be made today in the perinatal period, as it can be made in children and adults. Palliative care, rather than curative treatment, may be considered in three clinical situations: babies born at the limits of viability, withholding/withdrawing treatments in the NICU, and babies with severe malformations of genetic abnormalities identified during pregnancy. Only the last situation is addressed hereafter. In newborn infants as in older patients, palliative care aims at taking care of the baby and at providing comfort and well-being. The presence of human beings by the newborn infant, most importantly the parents and family, is of utmost importance. The available time should not be used only for care and medical treatments. Sufficient time should be kept for the parents to interact with the baby and for human presence and warmth. The best interests of the newborn infant are the main element for guiding appropriate care. Before birth, the choice of palliative care for newborn infants requires successive steps: (1) establishing a diagnosis of malformation(s) or genetic abnormalities; (2) making a prognosis and ruling out intensive treatments at birth and thereafter; (3) giving the parents appropriate information; (4) assisting the pregnant woman in deciding to continue pregnancy while excluding intensive treatment of the newborn baby; (5) dialoguing with parents about the expected duration of the baby’s life and the related uncertainty; (6) planning of palliative care to be implemented at birth; (7) preparing a plan with the parents for discharging the infant from the hospital and for taking care of him over a long time, when it is deemed possible that the baby may live for more than a few days.