Checkpoint inhibitor therapy constitutes a promising cancer treatment strategy that targets the immune checkpoints to re-activate silenced T cell cytotoxicity. In recent pivotal trials, immune checkpoint blockade (ICB) demonstrated durable responses and acceptable toxicity, resulting in the regulatory approval of 8 checkpoint inhibitors to date for 15 cancer indications. However, up to ~85% of patients present with innate or acquired resistance to ICB, limiting its clinical utility. Current response biomarker candidates, including DNA mutation and neoantigen load, immune profiles, as well as programmed death-ligand 1 (PD-L1) expression, are only weak predictors of ICB response. Thus, identification of novel, more predictive biomarkers that could identify patients who would benefit from ICB constitutes one of the most important areas of immunotherapy research. Aberrant DNA methylation (5mC) and hydroxymethylation (5hmC) were discovered in multiple cancers, and dynamic changes of the epigenomic landscape have been identified during T cell differentiation and activation. While their role in cancer immunosuppression remains to be elucidated, recent evidence suggests that 5mC and 5hmC may serve as prognostic and predictive biomarkers of ICB-sensitive cancers. In this review, we describe the role of epigenetic phenomena in tumor immunoediting and other immune evasion related processes, provide a comprehensive update of the current status of ICB-response biomarkers, and highlight promising epigenomic biomarker candidates.