The central topic of this review concerns the species XO, where X is F, Cl, Br or I. These molecules are thus the radicals FO, ClO, BrO and IO, but attention is also given to some of their precursors in the laboratory and the atmosphere, as well as to their reservoirs, sinks, and other related species of potential atmospheric importance. Laboratory data on the physics and chemistry of the species and atmospheric determinations of their concentrations are both considered. One aim of the review is to highlight the relationship between the laboratory investigations and the atmospheric studies. The emphasis of the review is on gas-phase processes. After a brief introductory section, the review continues with an examination of laboratory techniques for the study of the halogen-oxide species. This section fast looks at the general properties of the oxides and sources of them for laboratory experiments, then discusses the detection and measurement of the monoxide radicals in the laboratory, and ends with a description of the kinetic tools that have been harnessed in the various studies. The spectroscopy, structure, photochemistry and thermochemistry, of the halogen oxides are discussed in Section III. Both experimental and theoretical aspects are presented. The objectives of the work described are on the one hand to establish the basis for the detection of the radical and the measurement of its concentration in the laboratory and in the atmosphere, and on the other to provide the framework for interpreting pathways, mechanisms and efficiencies of photochemical and thermal reactions. Sections IV, V and VI of the review address the main issues of observed chemistry and its kinetics. Section IV gathers together available kinetic and mechanistic information on gas-phase reactions of FO, ClO, BrO and IO radicals, and the available data are summarized in appropriate tables. Section V reports on the corresponding data available for the gas-phase reactions of certain species containing the XO grouping, which include most of the so-called atmospheric reservoirs of XO radicals. There are three sub-sections, which deal in turn with oxide species, HOX, and XONO 2. Heterogeneous processes are introduced in Section VI. Heterogeneous chemistry in the atmosphere is that which occurs on or in ambient condensed phases that are in contact with the gas phase, such as aerosols, clouds, surface waters, and so on. It is becoming increasingly clear that such processes are of importance not only in the stratosphere, but also in the troposphere. Section VII of the review is concerned directly with the atmosphere. The sources and sinks of the compounds, the reaction pathways, temporary and permanent reservoirs, observational evidence, the involvement of the species in atmospheric chemistry, and modelling studies are considered for the troposphere and the stratosphere in turn. The section concludes with a more detailed exposition of the role of modelling of the halogen compounds in the stratosphere. The review concludes with an examination of issues in regard to the halogen oxide species that are unresolved, uncertain, or in need of further research. Further data are required, for example, on the spectroscopy and photochemistry of reservoir compounds, on potential organic sources of atmospheric iodine, and even on the channels for photolysis of compounds such as OClO. Within the field of reaction kinetics, there is a need for further study of the kinetics of dimer formation, and of certain other reactions of the radicals themselves (especially of IO) and some of their reservoirs. A substantial number of problems in heterogeneous chemistry of the species remain to be solved. Not only are some key physical measurements missing, but most of what has been achieved in both chemistry and physics is limited to chlorine-containing species, so that the work needs to be extended to the other halogens. There is also a need for a search for novel reactions occurring on conventional surfaces and for all types of reaction occurring on surfaces that exist within the atmosphere but which have not yet been the subject of laboratory study. So far as the atmosphere itself is concerned, there are important issues to be resolved. They include (i) the involvement of halogen species in episodic tropospherec ozone depletion in the Arctic (and a further question about whether or not such depletion is more widespread); (ii) the role of an active halogen chemistry in the oxidation of VOC; (iii) the significance and detail of stratospheric iodine and iodine-catalysed ozone removal; and (iv) the quantitative description of heterogeneous stratospheric chemistry.