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As the Universe evolves, it develops a web of filamentary structure of matter. This cosmic web is filled with gas, with the most diffuse gas lying in the intergalactic regions. At low redshift, the gas is predominantly warm-hot, and one of its best tracers is X-ray absorption in sightlines to background quasars. In this Chapter, we present the theoretical background for the formation of the warm-hot intergalactic medium (WHIM) and present the physical properties of the WHIM from cosmological hydro-dynamical simulations. We discuss the feasibility of detecting the WHIM with X-ray absorption lines, with high-resolution and high signal-to-noise spectra. We present detailed discussion of observing techniques, including the WHIM ionization balance, observable lines, the curve of growth, and the diagnostics using the X-ray lines. We present the current efforts of detecting the WHIM with gratings on-board Chandra and XMM-Newton observatories. We discuss the criticality of WHIM detections reported in literature, where robust detections are likely from the circumgalactic medium of intervening galaxies, or intra-group medium, rather than truly diffuse gas in the intergalactic medium. Secure detections of the most diffuse gas in the low redshift large scale structure may have to await next generation of X-ray telescopes. We end our Chapter with the discussion of future missions carrying dispersive and non-dispersive spectrometers. We present figure-of-merit parameters for line detectibility as well as for the number of WHIM systems that can be detected with future missions. These will define our ability to account for the missing low-redshift baryons and to understand the evolution of the Universe over half of its life.