Detecting HI using redshifted Ly-alpha absorption lines is 1e6 times more sensitive than using the 21cm emission line. We review recent discoveries of HI Ly-alpha absorbers made with the Hubble Space Telescope (HST) which have allowed us a first glimpse at gas in local intergalactic space between us and the ``Great Wall. Despite its mere 2.4m aperture, HST can detect absorbers with column densities as low as those found using Keck at high-z (log N(HI)=12.5 1/cm**2). New results that will be discussed include: the evolution of absorbers with redshift, the location of absorbers relative to galaxies (including the two-point correlation function for absorbers), the metallicity of absorbers far from galaxies, and the discovery of hot 1e5-1e6 K (shock-heated?) absorbers. The unique ability of VLA HI observations in discovering the nearest galaxies to these absorbers is stressed.