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Oversolubility effects refer to a large increase of the solubility of gases in liquids confined in nanoporous solids with respect to the value predicted by Henry's law. This review presents the state of the art of oversolubility by discussing the molecular mechanisms responsible for such effects and the conditions for their observation. Both experimental and theoretical approaches are reviewed, in a non-exhaustive fashion, with special emphasis on results that have helped to unravel the oversolubility phenomenon. Different porous materials including metal-organic frameworks (MOF), ordered porous silicas, and zeolites are considered in combination with various nanoconfined liquids and gases relevant to practical applications in energy and environmental science. Depending on the gas/liquid/solid system considered, oversolubility is shown to pertain either to adsorption (increased concentration at solid/gas and liquid/gas interfaces) or to confinement-induced solubility increase. We also critically discuss when oversolubility effects are expected to lead to improved performance in catalysis or environmental applications such as for air purification. Image 1 • We present the state of the art on oversolubility in nanoporous materials. • Molecular mechanisms are presented and discussed. • Both experimental and theoretical approaches are reviewed with special emphasis on results that have helped unravel the oversolubility phenomenon. • We provide suggestions for future investigations and application perspectives. [ABSTRACT FROM AUTHOR]