  The local HI mass function (HIMF), like the optical luminosity function, is
an important observational input into models of cosmology and galaxy evolution.
It is a helpful framework for assessing the number density of gas rich dwarf
galaxies, which are easily missed in optically selected galaxy samples, as well
as for determining the cosmological density of neutral gas at the present
epoch. For HI masses larger than 10^8 M_solar the HIMF is determined with
reasonable accuracy and the same function is obtained from both optical and HI
selected samples of galaxies. However, the faint tail below M_HI = 10^7 M_solar
is still ill-constrained and leaves room for a population of gas rich dwarfs or
free floating HI clouds which hypothetically could contribute significantly to
the local gas density. Determining the faint tail far below HI masses of 10^7
M_solar will be a great challenge for the future.
