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 to study the low-redshift, low-mass, gas-rich dwarf galaxy
population discovered by ALFALFA.  The centerpiece of this effort is the
Survey of HI in Extremely Low-mass Dwarfs (SHIELD). SHIELD is an ongoing
multi-wavelength investigation of the properties of 12 extremely low-mass
galaxies selected from an early ALFALFA data release.  I will present
preliminary SHIELD results from imaging and spectroscopic observing
campaigns with the VLA, HST, Spitzer, GALEX, and WIYN telescopes.  I will
then discuss results from parallel ongoing observing programs that fully
exploit the faint end of the galaxy mass function derived by ALFALFA.
These efforts include surveys of "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 the extreme galaxy Leo P, one
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 extremely low-mass regime.