The "Satellites Around Galactic Analogs" (SAGA) Survey is a spectroscopic survey that aims to discover and identify dwarf galaxy satellite systems around Milky Way-like galaxies outside the Local Volume. The Survey measures the satellite luminosity function in these systems down to the brightness of the Leo I galaxy, and also the star formation rate of these satellite galaxies. To date we have measured more than 17,000 spectra, identified more than 100 satellite galaxies, and obtained complete coverage around 21 host galaxies. The unprecedented datasets provide us new understandings of our own Galaxy in a cosmological context, and supply crucial ingredients for the study of galaxy formation and the nature of dark matter. In this talk, I will describe the design, progress, and current results of the SAGA Survey. I will also discuss how SAGA results, together with theoretical models that we develop, improve our understanding of the galaxy-halo connection at small scales, which in turn allows us to fully utilize astrophysical observations to probe the nature of dark matter.