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This efficient satellite quenching is particularly striking because, other than KKR 25 and KKs 3, at $\mstar<10^9\msun$ all known galaxies that are sufficiently isolated ($>1500\kpc$ from a more massive galaxy) are star-forming \citep{Geha2012, Phillips2014}.  Thus, the MW and M31 halos show the strongest signal of environmental influence over their satellites of any known systems, and the LG is a compelling laboratory for studying environmental processes on galaxies.  Several such processes within a host halo can regulate the gas content, star formation, morphology, and eventual disruption of satellite galaxies, including gravitational tidal forces \citep[e.g.,][]{Dekel2003}, galaxy-galaxy tidal interactions \citep[e.g.,][]{FaroukiShapiro1981}, galaxy-galaxy mergers \citep[e.g.,][]{Deason2014a}, and ram-pressure stripping of extended gas \citep[e.g.,][]{Larson1980, McCarthy2008} or cold inter-stellar medium \citep[e.g.,][]{GunnGott1972, Tonnesen2009}, some of which may be assisted by stellar feedback within the satellite \citep[e.g.,][]{BaheMcCarthy2015}. \citep[e.g.,][]{NicholsBlandHawthorn2011,BaheMcCarthy2015}.  %tidal shocking and resonant interactions with the host \citep[e.g.,][]{Mayer2001,DOnghia2010},   The key astrophysical challenge is understanding the relative importance of these processes, including which (if any) dominate, and how they vary across both satellite and host masses.