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A thin veneer of atmosphere, soil, and water covers the surface of the planet. That is the envelope supplying most of the raw material we need to live. Energy from the Sun, with some residual energy still within the planet’s core, feeds Earth’s dynamic systems that cycle materials within the envelope. Earth System scientists are investigating the energy and material fluxes that determine the systems’ dynamics to better understand climate change. This Compendium presents some of the vanguard science and conceptual advances under discussion and published by researchers since 2007 that explores the challenge presented by climate change. Rapidly developing tools—that allow fast and accurate readings of environmental conditions, that compile and analyze data series of increasing complexities at unprecedented rates, and that allow insights into fluxes of energy and material at micro and macro scales—have accelerated the rate at which vanguard science is being produced.