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Galaxies in denser environments are more likely to have suppressed (quiescent) star formation and little-to-no cold gas than galaxies of similar stellar mass, $\mstar$, in less dense environments.  The observed environmental effects in the Local Group (LG), specifically on the satellite galaxies within the halos of the Milky Way (MW) and Andromeda (M31), are particularly strong \citep[e.g.,][]{Einasto1974,Mateo1998,GrcevichPutman2009,McConnachie2012,Phillips2014,SlaterBell2014,Spekkens2014}, even compared to the effects on (more massive) satellites within massive groups/clusters.  Specifically, the dwarfs dwarf galaxies  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 spheroidal morphologies, (2) having most of their baryonic mass in cold atomic gas to having little-to-no measured cold gas, and (3) being actively star-forming to quiescent. This trend has just a few exceptions: 4 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 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{Lewis2007, Fraternali2009, Teyssier2012}.  This efficient satellite quenching is particularly striking because, other than KKR 25, at $\mstar<10^9\msun$ \emph{all} known galaxies that are sufficiently isolated ($>1500\kpc$ from a more massive galaxy) are star-forming \citep{Geha2012, Phillips2014}. \textbf{XXX Not sure I agree with this claim -- as I show in Weisz et al. 2015, if you look at the Karachentsev catalog of nearby galaxies (Karachentsev et al. 2013), there are more dSphs in the field than this XXX -- I would say that *most* dSphs that we know of are located near a massive host -- but there are probably significant selection effects here}.   Thus, the MW and M31 halos exert the strongest environmental influence on their satellites of any known systems, so the LG is the most compelling laboratory for studying environmental processes on galaxies.