The Sunyaev-Zeldovich (SZ) effect was first predicted nearly five decades ago, but has only recently become a mature tool for performing high resolution studies of the warm and hot ionized gas in and between galaxies, groups, and clusters. Galaxy groups and clusters are powerful probes of cosmology, and they also serve as hosts for roughly half of the galaxies in the Universe. In this white paper, we outline the advances in our understanding of thermodynamic and kinematic properties of the warm-hot universe that can come in the next decade through spatially and spectrally resolved measurements of the SZ effects. Many of these advances will be enabled through new/upcoming millimeter/submillimeter (mm/submm) instrumentation on existing facilities, but truly transformative advances will require construction of new facilities with larger fields of view and broad spectral coverage of the mm/submm bands.
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