Oxygen is an essential element of aerobic life, and oxidative metabolism represents a principal source of energy. Nevertheless, oxygen may also be toxic and mutagenic with the potential to cause damage through the production of reactive oxygen species (ROS). ROS generation can be considered a double-edged sword. Beneficial effects of ROS occur at moderate concentrations and involve physiological roles in cellular responses to noxia, as in defense against infectious agents, in the function of a number of cellular signaling pathways and the induction of a mitogenic response. The overproduction of ROS and the insufficiency of an antioxidant mechanism results in oxidative stress (OS), a deleterious process and important mediator of damage to cell structures and tissues. Newborns, especially if preterm, are particularly susceptible to OS and damage due to increased generation of ROS, the lack of adequate antioxidant protection, and the inability to induce antioxidant defenses during the hyperoxic challenge at birth. Hence the “Oxygen Paradox”: higher eukaryotic aerobic organisms cannot exist without oxygen and without OS, yet oxygen and ROS are dangerous to their existence. Originally, the oxygen paradox described that the injury was aggravated by giving oxygen after hypoxia. Today, we know this is caused by production of oxygen radicals. Therefore, it is mandatory in the handling of newborns to use oxygen as a medication when clinical surveillance indicates a need.