Elevated mitochondrial matrix superoxide and/or hydrogen peroxide concentrations drive a wide range of physiological responses and pathologies. Concentrations of superoxide and hydrogen peroxide in the mitochondrial matrix are set mainly by rates of production, the activities of superoxide dismutase-2 (SOD2) and peroxiredoxin-3 (PRDX3), and by diffusion of hydrogen peroxide to the cytosol. These considerations can be used to generate criteria for assessing whether changes in matrix superoxide or hydrogen peroxide are both necessary and sufficient to drive redox signaling and pathology: is a phenotype affected by suppressing superoxide and hydrogen peroxide production; by manipulating the levels of SOD2, PRDX3 or mitochondria-targeted catalase; and by adding mitochondria-targeted SOD/catalase mimetics or mitochondria-targeted antioxidants? Is the pathology associated with variants in SOD2 and PRDX3 genes? Filtering the large literature on mitochondrial redox signaling using these criteria highlights considerable evidence that mitochondrial superoxide and hydrogen peroxide drive physiological responses involved in cellular stress management, including apoptosis, autophagy, propagation of endoplasmic reticulum stress, cellular senescence, HIF1a signaling, and immune responses. They also affect cell proliferation, migration, differentiation, and the cell cycle. Filtering the huge literature on pathologies highlights strong experimental evidence that 30-40 pathologies may be driven by mitochondrial matrix superoxide or hydrogen peroxide. These can be grouped into overlapping and interacting categories: metabolic, cardiovascular, inflammatory, and neurological diseases; cancer; ischemia/reperfusion injury; aging and its diseases; external insults, and genetic diseases. Understanding the involvement of mitochondrial matrix superoxide and hydrogen peroxide concentrations in these diseases can facilitate the rational development of appropriate therapies.