The aim of this paper is to review recent progress in detection and quantification of hydroperoxides, and to understand their reaction kinetics in combustion environments. Hydroperoxides, characterized by an-OOH group, are ubiquitous in the atmospheric oxidation of volatile organic compounds (~300 K), and in the liquid and gas phase oxidation of fuel components at elevated temperatures (~400-1000 K). They are responsible for two-stage fuel ignition in internal combustion engines and they play an important role in the formation and evolution of secondary organic aerosols in the atmosphere. The introduction outlines the importance of hydroperoxide chemistry in combustion reaction processes. In addition to this main topic, the role of hydroperoxide in atmospheric and liquid phase oxidation chemistry is also introduced, for a more general perspective. The second part of this paper briefly reviews the mechanistic insights of hydroperoxide chemistry in combustion systems, including experimental detection of these reactive species before 2010. Since that time significant progress has been made by advanced diagnostic techniques like tunable synchrotron vacuum ultraviolet photoionization mass spectrometry and infrared cavity ring-down spectroscopy. The third chapter of this work summarizes progress in gas phase oxidation experiments to measure hydrogen peroxide, alkyl hydroperoxides, olefinic hydroperoxides, ketohydroperoxides, and more complex hydroperoxides that include as many as five oxygen atoms. The fourth section details recent advances in understanding the combustion chemistry of hydroperoxides, involving the formation of carboxylic acids and diones, as well as the development of oxidation models that include a third O2 addition reaction mechanism. Finally, challenges are discussed, and perspectives are offered regarding the future of accurately measuring molecule-specific hydroperoxide concentrations and understanding their respective reaction kinetics.