Cellular senescence, an irreversible growth arrest triggered by a variety of stressors, plays important roles in normal physiology and tumor suppression, but accumulation of senescent cells with age contributes to the functional decline of tissues. Senescent cells undergo dramatic alterations to their chromatin landscape that affect genome accessibility and their transcriptional program. These include the loss of DNA-nuclear lamina interactions, the distension of centromeres, and changes in chromatin composition that can lead to the activation of retrotransposons. Here we discuss these findings, as well as recent advances in microscopy and genomics that have revealed the importance of the higher-order spatial organization of the genome in defining and maintaining the senescent state.