Plants are not only obligate aerobic organisms requiring oxygen for mitochondrial energy production, but also produce oxygen during photosynthesis. Therefore, plant cells have to cope with a hyperoxic cellular environment that determines a production of reactive oxygen species (ROS) higher than the one occurring in animal cells. In order to maintain redox homeostasis under control, plants evolved a particularly complex and redundant ROS-scavenging system, in which enzymes and metabolites are linked in a network of reactions. This review gives an overview of the mechanisms active in plant cells for controlling redox homeostasis during optimal growth conditions, when ROS are produced in a steady-state low amount, and during stress conditions, when ROS production is increased. Particular attention is paid to the aspects of oxygen/ROS management for which plant and animal cells differ.