Chromatin, the spatial organizer of genomic DNA, is hierarchically folded into higher-order structures to facilitate DNA compaction, enabling genome surveillance. Understanding the organization and function of the three-dimensional (3D) genome is critical to profile chromatin accessibility and functional interactions that govern gene regulation across multiple biological processes, including aging and one of its hallmarks, cellular senescence. Cellular senescence constitutes a defensive stress response to various intrinsic and extrinsic stimuli, preserving cellular and organismal homeostasis through a generally irreversible cell cycle arrest. In this review article we discuss epigenetic alterations occurring to DNA and chromatin that drive and fuel the onset of this complex phenomenon. As such, we describe major large-scale chromatin events, including the formation of higher-order chromatin structures and the 3D spatial alterations of the genome that occur during senescence. We also discuss global heterochromatin loss, deficiencies in nuclear lamins, the depletion of core histones and their modifications, as well as the epigenetic regulation of the senescence-associated secretory phenotype (SASP), all of which serve key roles in the epigenome of senescent cells. To clearly demonstrate the significance of epigenetic modifications, data from a computational meta-analysis are presented, aiming to further underpin key epigenetic mechanisms occurring in senescent cells. Last, we highlight promising epigenetic modulators implemented in therapeutic strategies for senescent cell detection and elimination, possibly leading to significant clinical advances against various age-related diseases as well as the delay and prevention of the aging onset.