Abstract At low redshift, only about one-tenth of the known baryons lie in galaxies or the hot gas seen in galaxy clusters and groups. Models posit that these “missing baryons” are in gaseous form in overdense filaments that connect the much denser virialized groups and clusters. About 30% is cool (<10⁵ K) and is detected in Lyα absorption studies, but about half is predicted to lie in the 10⁵–10⁷ K regime. Gas is detected in the 2–5 × 10⁵ K range through OVI absorption studies (7% of the baryons) and possibly near 10⁵ K from broad Lyα absorption (20% of the baryons). Hotter gas (0.5–2 × 10⁶ K) is detected at zero redshift by OVII and OVIII Kα X-ray absorption, and the OVII line strengths seem to correlate with the Galactic soft X-ray background, so it is probably produced by Galactic halo gas, rather than a Local Group medium. There are no compelling detections of the intergalactic hot gas (0.5–10 × 10⁶ K) either in absorption or emission and these upper limits are consistent with theoretical models. Claimed X-ray absorption lines are not confirmed, while most of the claims of soft emission are attributable to artifacts of background subtraction and field-flattening. The missing baryons should become detectable with moderate improvements in instrumental sensitivity.