The Faint End of the HI Mass Function

Low-mass galaxies are the most numerous type of extragalactic system at all epochs of the universe. The population of low-mass galaxies in the local volume allows unique astrophysical and cosmological perspectives that are unavailable in more distant or more massive systems. The ALFALFA blind extragalactic HI survey has cataloged tens of thousands of gas-rich galaxies in the local universe and has populated the faint end of the HI mass function with statistical confidence for the first time. In this talk I will present results from comprehensive follow-up observing campaigns designed to study the low-redshift, low-mass, gas-rich population discovered by ALFALFA. The centerpiece of this effort is the Survey of HI in Extremely Low-mass Dwarfs (SHIELD), an ongoing multi-wavelength investigation of the properties of 82 extremely low-mass galaxies selected from the complete ALFALFA catalog. I will also discuss results from parallel ongoing observing programs that explore more exotic low-mass objects, including "ultra compact high velocity clouds" (HI clouds with structural parameters that match those of gas-bearing "mini-halos" if located within ~1 Mpc), candidate "dark galaxies" (systems with extreme hydrogen mass to stellar light ratios), and targeted studies of individual sources of interest (including two of the most metal-poor galaxies known in the universe). Taken as a whole, these observing programs are furthering our understanding of the continuum of galaxy properties in the low-mass regime.