Maintaining genome stability is essential to an organism’s health and survival. Breakdown of the mechanisms protecting the genome and the resulting genome instability are an important aspect of the aging process and have been linked to diseases such as cancer. Thus, a large network of interconnected pathways is responsible for ensuring genome integrity in the face of the continuous challenges that induce DNA damage. While these pathways are diverse, epigenetic mechanisms play a central role in many of them. DNA modifications, histone variants and modifications, chromatin structure, and non-coding RNAs all carry out a variety of functions to ensure that genome stability is maintained. Epigenetic mechanisms ensure the functions of centromeres and telomeres that are essential for genome stability. Epigenetic mechanisms also protect the genome from the invasion by transposable elements and contribute to various DNA repair pathways. In this review, we highlight the integral role of epigenetic mechanisms in the maintenance of genome stability and draw attention to issues in need of further study.