The Criegee intermediates, carbonyl oxides proposed by Criegee in 1949 as key intermediates in the ozonolysis of alkenes, play important roles in many aspects of atmospheric chemistry. Because direct detection of these gaseous intermediates was unavailable until recently, previous understanding of their reactions, derived from indirect experimental evidence, had great uncertainties. Recent laboratory detection of the simplest Criegee intermediate CH2OO and some larger members, produced from ultraviolet irradiation of corresponding diiodoalkanes in O2, with various methods such as photoionization, ultraviolet absorption, infrared absorption, and microwave spectroscopy opens a new door to improved understanding of the roles of these Criegee intermediates. Their structures and spectral parameters have been characterized; their significant zwitterionic nature is hence confirmed. CH2OO, along with other products, has also been detected directly with microwave spectroscopy in gaseous ozonolysis reactions of ethene. The detailed kinetics of the source reaction, CH2I + O2, which is critical to laboratory studies of CH2OO, are now understood satisfactorily. The kinetic investigations using direct detection identified some important atmospheric reactions, including reactions with NO2, SO2, water dimer, carboxylic acids, and carbonyl compounds. Efforts toward the characterization of larger Criegee intermediates and the investigation of related reactions are in progress. Some reactions of CH3CHOO are found to depend on conformation. This perspective examines progress toward the direct spectral characterization of Criegee intermediates and investigations of the associated reaction kinetics, and indicates some unresolved problems and prospective challenges for this exciting field of research.