The problem of prematurity is increasing in the world with the prevalence of 18% in some African countries and 5% in some European countries and more than 15 million of premature babies born every year. The survival of premature infants is dependent on the gestational age and the birthweight, development of the country and availability of neonatal intensive care. If a premature baby is born before 28 gestational weeks and neonatal intensive care is not available, then the probability of dying is up to 95%. This chapter examines issues of the limits of viability from the medical and ethical point of view, considering the data and way of thinking in developed countries. This chapter covers the survival at the limits of viability from the historical point of view and recently, main issues connected with the survival of infants at the limits of viability, ethical dilemmas in the care for infants at the limits of viability, right of the newborn to be born in the best possible conditions, management of premature infants, and environmental hypothesis of intrauterine life.