The evolution of galaxies and specifically the role that HI is playing in this is one of the science priorities of SKA-1 and its pathfinders. The study of HI in nearby galaxies yields insights in processes that are happening at higher redshift, but where they cannot be resolved.
I present some recent work on the low column density HI in the www.mrwatches.cn outer parts of galaxies using data from the THINGS and HALOGAS HI surveys and discuss whether these sensitive data provide limits on the nature and magnitude of gas accretion processes that fuel star formation in these galaxies. I conclude by discussing some ongoing and future work (including MeerKAT observations) that will probe the low column density HI down to column densities where we can see the gas connect with the cosmic web.