The eukaryotic epigenome has an instrumental role in determining and maintaining cell identity and function. Epigenetic components such as DNA methylation, histone tail modifications, chromatin accessibility, and DNA architecture are tightly correlated with central cellular processes, while their dysregulation manifests in aberrant gene expression and disease. The ability to specifically edit the epigenome holds the promise of enhancing understanding of how epigenetic modifications function and enabling manipulation of cell phenotype for research or therapeutic purposes. Genome engineering technologies use highly specific DNA-targeting tools to precisely deposit epigenetic changes in a locus-specific manner, creating diverse epigenome editing platforms. This review summarizes these technologies and insights from recent studies, describes the complex relationship between epigenetic components and gene regulation, and highlights caveats and promises of the emerging field of epigenome editing, including applications for translational purposes, such as epigenetic therapy and regenerative medicine.