The extended environment of galaxies contains a wealth of information about the formation and life cycle of galaxies which are regulated by accretion and feedback processes. Observations of neutral hydrogen are routinely used to image the high brightness disks of galaxies and to study their kinematics. Deeper observations will give more insight into the distribution of diffuse gas in the extended halo of the galaxies and the inter-galactic medium, where numerical simulations predict a cosmic web of extended structures and gaseous filaments. To observe the extended environment of galaxies, column density sensitivities have to be achieved that probe the regime of Lyman limit systems. HI observations are typically limited to a brightness sensitivity of NHI~10^19^cm^-2^, but this must be improved upon by ~2 orders of magnitude.