Abstract. Unpredicted observations in the climate system, such as recent excessive ocean warming, are often lacking immediate causal explanations and are challenging numerical models. As a highly advanced mathematical tool, the Thermodynamic Equation of Seawater – 2010 (TEOS-10) was established by international bodies as an interdisciplinary standard and is recommended for use in geophysics, such as, and in particular, in climate research. From its very beginning, the development of TEOS-10 was supported by Ocean Science through publishing successive stages and results. Here, the history and properties of TEOS-10 are briefly reviewed. With focus on the air–sea interface, selected current problems of climate research are discussed, and tutorial examples for the possible use of TEOS-10 in the associated context are presented, such as topics related to ocean heat content, latent heat, and the rate of marine evaporation; properties of sea spray aerosol; or climatic effects of low-level clouds. Appended to this article, a list of publications and their metrics is provided for illustrating the uptake of TEOS-10 by the scientific community, along with some continued activities, addressing still pending, connected issues such as uniform standard definitions of uncertainties of relative humidity, seawater salinity, or pH. This article is dedicated to the jubilee celebrating 20 years of Ocean Science. This article is also dedicated to the memory of Wolfgang Wagner, who sadly and unexpectedly passed away on 12 August 2024. His contributions to TEOS-10 are truly indispensable constituents; Wolfgang was an essential co-author of various related documents and articles. He will be deeply missed. All the rivers run into the sea; yet the sea is not full; unto the place from whence the rivers come, thither they return again. The King James Bible: Ecclesiastes, 450–150 BCE He wraps up the waters in his clouds, yet the clouds do not burst under their weight. Holy Bible: New International Version, Job 26:8 Of the air, the part receiving heat is rising higher. So, evaporated water is lifted above the lower air. Leonardo da Vinci: Primo libro delle acque, Codex Arundel, ca. 1508 Two-thirds of the Sun's energy falling on the Earth's surface is needed to vaporize … water … as a heat source for a gigantic steam engine. Heinrich Hertz: Energiehaushalt der Erde, 1885 The sea-surface interaction is obviously a highly significant quantity in simulating climate. Andrew Gilchrist and Klaus Hasselmann: Climate Modelling, 1986 The climate of the Earth is ultimately determined by the temperatures of the oceans. Donald Rapp: Assessing Climate Change, 2014