Reactive oxygen species (ROS) are by-products of normal cell activity. They are produced in many cellular compartments and play a major role in signaling pathways. Overproduction of ROS is associated with the development of various human diseases (including cancer, cardiovascular, neurodegenerative, and metabolic disorders), inflammation, and aging. Tumors continuously generate ROS at increased levels that have a dual role in their development. Oxidative stress can promote tumor initiation, progression, and resistance to therapy through DNA damage, leading to the accumulation of mutations and genome instability, as well as reprogramming cell metabolism and signaling. On the contrary, elevated ROS levels can induce tumor cell death. This review covers the current data on the mechanisms of ROS generation and existing antioxidant systems balancing the redox state in mammalian cells that can also be related to tumors.