Polycomb repressive complex 2 (PRC2) is a conserved multisubunit enzyme that methylates histone H3 on lysine-27. This chromatin modification is a hallmark of target genes transcriptionally silenced by the Polycomb system. At its core, PRC2 activity depends upon the SET domain active site of its catalytic subunit, EZH2, as well as critical stimulatory inputs from noncatalytic subunits, especially EED and SU(Z)12. We review recent progress on this core PRC2 machinery, including key features of the active site, control mechanisms that operate via EZH2 phosphorylation, and subunit elements and architectures that influence PRC2 function. Among these, we highlight work identifying an EED regulatory site that enables PRC2 to bind pre-existing methylated H3-K27 and stimulate enzyme output. These advances illuminate basic inner workings of PRC2 and also provide insights that could aid design of PRC2 inhibitors. The chromatin landscape that PRC2 encounters in vivo is decorated with many histone modifications that accompany active transcription, such as H3-K4 methylation. It has long been assumed that these "active" modifications oppose PRC2 at some level but, until recently, mechanisms of this antagonistic cross-talk have been elusive. We discuss new findings that illuminate how H3-K4 and H3-K36 methylation, H3-K27 acetylation, and H3-S28 phosphorylation each exert a negative impact on PRC2 function. The emerging picture presents PRC2 as a cooperative multipart machine, intricately outfitted to sense and respond to the local chromatin environment and other cues. This PRC2 design ensures flexibility and fine tuning of its fundamental gene silencing roles in diverse biological contexts.