A wide variety of aromatic compounds are aerobically degraded by bacteria. Aromatic-ring hydroxylation is one of the most common initial degradation step and thus is an essential catalytic reaction for aromatic-ring degradation by bacteria in nature. Most of the cases, the hydroxylation is catalyzed by an oxygenase family known as Rieske nonheme iron (di)oxygenase or Rieske oxygenase (RO). ROs catalyze a broad range of aromatic-ring compounds including mono- and polycyclic aromatic and hetero-aromatic compounds. ROs are composed of terminal oxygenase and electron transfer components. The terminal oxygenase component has Rieske [2Fe-2S] cluster as a redox center for receive electrons from the electron transfer component(s) and mononuclear iron as a catalytic site for dioxygen activation. In addition to genetic and biochemical studies, their crystal structures have been extensively studied recently. To date (11/7/2012), the structures of 15 different terminal oxygenases and 11 electron transfer components have been determined and deposited to Protein Data Bank (76 structures including their variants in total). This chapter will address structures and functions of aromatic-ring hydroxylating dioxygenases. The overviews of ROs (Sect. 9.1) and overall structure of ROs containing their electron transfer components (Sect. 9.2), inter- and intramolecular electron transfer in ROs (Sect. 9.3), catalytic mechanism (Sect. 9.4), and substrate specificity and enzyme engineering (Sect. 9.5) are reviewed.