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The observed environmental effects in the Local Group (LG), specifically on the satellite dwarf galaxies within the halos of the Milky Way (MW) and Andromeda (M31), are particularly strong \citep[e.g.,][]{Einasto1974,Mateo1998,McConnachie2012,Phillips2014,SlaterBell2014,Spekkens2014}, even compared to the effects on (more massive) satellites within massive groups/clusters.  Specifically, the dwarfs around the MW/M31 show a strikingly sharp and nearly complete transition in their properties within $\approx 300 \kpc$ (approximately the virial radius, $\rvir$, of the MW or M31), transitioning from (1) having irregular to elliptical/spheroidal morphologies, (2) having most of their baryonic mass in cold atomic/molecular gas to having little-to-no measured cold gas, and (3) being actively star-forming to quiescent \citep[e.g.,][and references therein]{McConnachie2012}.  This trend has just a few exceptions: four gas-rich, star-forming galaxies persist within the halos of the MW (the LMC and SMC) and M31 (LGS 3 and IC 10), and 3 - 4 quiescent, gas-poor galaxies reside just beyond $\rvir$ of the MW (Cetus and Tucana) and M31 (KKR 25 and possibly Andromeda XVIII), though Cetus and Tucana likely orbited within the MW halo \citep{Teyssier2012}.  This efficient satellite quenching is particularly striking because, other than KKR 25, at $\mstar<10^9\msun$ all known galaxies that are isolated (beyond $1500\kpc$ of a more massive galaxy) are star-forming \citep{Geha2012}. \citep{Geha2012, Phillips2014}.  Thus, the MW and M31 halos exert the strongest environmental influence on their satellites of any known systems, so the LG is perhaps the most compelling laboratory for studying environmental processes on galaxies.  Several environmental processes within a host halo regulate the gas content, star formation, morphology, and eventual tidal disruption of satellite galaxies, including gravitational tidal forces \citep[e.g.,][]{Dekel2003}, galaxy-galaxy interactions \citep[e.g.,][]{FaroukiShapiro1981} and mergers \citep[e.g.,][]{Deason2014a}, tidal shocking and resonant interactions with the host \citep[e.g.,][]{Mayer2001,DOnghia2010}, ram-pressure stripping of extended gas around the satellite \citep[e.g.,][]{Larson1980,McCarthy2008} of the cold inter-stellar medium \citep[e.g.,][]{GunnGott1972,Tonnesen2009}, many of which can be assisted by feedback from stars and/or AGN within the satellites \citep[e.g.,][]{BaheMcCarthy2015}.