Three decades of research on the biochemistry of peroxynitrite (ONOOH/ONOO−) have established that this stealthy oxidant is formed in biological systems, and that its main targets are carbon dioxide (CO2), metalloproteins and thiols (RSH). Peroxynitrous acid reacts directly with thiols (precisely, with thiolates, RS−), forming sulfenic acids (RSOH). In addition, the free radicals derived from peroxynitrite, mainly carbonate radical (CO3•−) and nitrogen dioxide (NO2•) formed from the reaction of peroxynitrite anion with CO2, oxidize thiols to thiyl radicals (RS•). These two pathways are under kinetic competition. The primary products of thiol oxidation can follow different decay routes; sulfenic acids usually react with other thiols forming disulfides, while thiyl radicals can react with oxygen, with other thiols and with other reductants such as ascorbic acid. Peroxynitrite is also able to oxidize hydrogen sulfide (H2S/HS−) and persulfides (RSSH/RSS−). Among the different biological thiols, peroxiredoxins stand out as main peroxynitrite reductases due to their very high rate constants of reaction with peroxynitrite together with their abundance. Rooted in kinetic concepts, evidence is emerging for the role of peroxiredoxins in peroxynitrite detoxification, with potential implications in diseases in which peroxynitrite is involved.