Substantial pieces of direct and indirect evidence have mounted over the years linking the induction of oxidative stress to a plethora of disease conditions, not least those associated with the death of neurons. The causal relationship between oxidative damage and neurodegeneration is, however, not yet clear and still a subject of intense investigation. Nevertheless, the phenomenon of oxidative neuronal death has received considerable attention in a frantic search for efficacious therapies for the management of neurological and neurodegenerative conditions. The redox-active nature of reactive oxygen species (ROS), which in their excessive levels induce oxidative stress, the prevalence of ROS production in biological systems, the complexity of interrelationships among these species, and the context-dependent adequacy and resilience of the antioxidant defense systems are some of the challenges that basic research has to grapple with to advance successfully to the translational stage. Much still has to be understood for research efforts in this field to yield enduring therapies. In this review, we examine the nature (chemistry) of ROS, the relationships between them, their physiological functions, the roles of oxidative stress in neurodegeneration, the mechanisms of cell death induced by oxidant species, and the available means of protecting neurons against oxidative damage.