The first image of a Cosmic Web , Lyman Limit System has just been made in HI emission within the Local Group filament connecting M31 and M33 . The corresponding HI distribution function is in very good agreement with that of the QSO absorption lines , confirming the 30-fold increase in surface area expected between 10 ^ { 19 } cm ^ { -2 } and 10 ^ { 17 } cm ^ { -2 } . The critical observational challenge is crossing the “ HI desert ” , the range of log ( N _ { HI } ) from about 19.5 down to 18 , over which photo-ionization by the intergalactic radiation field produces an exponential decline in the neutral fraction from essentially unity down to a few percent . Nature is kinder again to the HI observer below log ( N _ { HI } ) = 18 , where the neutral fraction decreases only very slowly with log ( N _ { HI } ) . Average spectra of the M31/M33 filament suggest a kinetic temperature of 2 \times 10 ^ { 5 } K for the parent ion population , consistent with significant shock-heating . The brightest knot within the filament , with only a 2 \times 10 ^ { 4 } K apparent temperature , is suggestive of localized cooling and condensation . We have initiated two complimentary surveys that should lay the groundwork for a comprehensive study of the Cosmic Web phenomenon in HI emission . When combined with targeted optical and UV absorption line observations , the total baryonic masses and enrichment histories of the Cosmic Web could be determined over the complete range of environmental over-densities .