The collision between the solar wind and the interstellar medium populates the heliosphere with hot hydrogen gas, especially in between the heliopause and bow shock. This hydrogen can produce detectable H I Lyman‐α absorption in Hubble Space Telescope (HST) observations of nearby stars. Lyman‐α absorption has also been detected from stellar astrospheres as well as for the heliosphere. I present here some new detections of heliospheric and astrospheric H I absorption that have resulted from an ongoing analysis of HST archival data.