Immune checkpoint inhibitors (ICIs) have demonstrated to be highly efficient in treating solid tumors; however, many patients have limited benefits in terms of response and survival. This rapidly led to the investigation of combination therapies to enhance response rates. Moreover, predictive biomarkers were assessed to better select patients. Although PD-L1 expression remains the only validated marker in clinics, molecular profiling has brought valuable information, showing that the tumor mutation load and microsatellite instability (MSI) status were associated to higher response rates in nearly all cancer types. Moreover, in lung cancer, EGFR and MET mutations, oncogene fusions or STK11 inactivating mutations were associated with low response rates. Cancer progression towards invasive phenotypes that impede immune surveillance relies on complex regulatory networks and cell interactions within the tumor microenvironment. Epigenetic modifications, such as the alteration of histone patterns, chromatin structure, DNA methylation status at specific promoters and changes in microRNA levels, may alter the cell phenotype and reshape the tumor microenvironment, allowing cells to grow and escape from immune surveillance. The objective of this review is to make an update on the identified epigenetic changes that target immune surveillance and, ultimately, ICI responses, such as histone marks, DNA methylation and miR signatures. Translational studies or clinical trials, when available, and potential epigenetic biomarkers will be discussed as perspectives in the context of combination treatment strategies to enhance ICI responses in patients with solid tumors.