The role of non-duplex DNA, the guanine-quadruplex structure in particular, is becoming widely appreciated. Increasing evidence in the last decade implicates quadruplexes in important processes such as transcription and replication. Interestingly, more recent work suggests roles for quadruplexes, in association with quadruplex-interacting proteins, in epigenetics through both DNA and histone modifications. Here, we review the effect of the quadruplex structure on post-replication epigenetic memory and quadruplex-induced promoter DNA/histone modifications. Furthermore, we highlight the epigenetic state of the telomerase promoter where quadruplexes could play a key regulatory role. Finally, we discuss the possibility that DNA structures such as quadruplexes, within a largely duplex DNA background, could act as molecular anchors for locally induced epigenetic modifications. Highlights G4s mediate promoter histone modifications. Recent work shows how G4 association of regulatory factors recruits chromatin modifiers, resulting in repressive histone modifications and gene repression. In the absence of designated helicases, G4s impede DNA replication. This partially delinks DNA replication from repackaging of newly made chromatin. As a result, fidelity in copying parental histone modifications is affected, compromising epigenetic memory. DNA methylation influences G4 stability, affecting transcription factor binding. At the telomerase promoter, C5 methylation occludes CTCF binding, de-repressing telomerase expression in cancer cells. Spotlight on tandem array of G4s within the telomerase promoter. These sequence stretches harboring potential G4s are key to the epigenetic status of the tightly repressed telomerase promoter in normal somatic cells and the aberrant high telomerase expression in cancer. [ABSTRACT FROM AUTHOR]