Myeloid cells play a vital role in innate immune responses as they recognize and phagocytose pathogens like viruses, present antigens, produce cytokines, recruit other immune cells to combat infections, and contribute to the attenuation of immune responses to restore homeostasis. Signal integration by pathogen recognition receptors enables myeloid cells to adapt their functions by a network of transcription factors and chromatin remodelers. This review provides a brief overview of the subtypes of myeloid cells and the main epigenetic regulation mechanisms. Special focus is placed on the epigenomic alterations in viral nucleic acids of HIV and SARS-CoV-2 along with the epigenetic changes in the host's myeloid cell compartment. These changes are important as they lead to immune suppression and promote the progression of the disease. Finally, we highlight some promising examples of 'epidrugs' that modulate the epigenome of immune cells and could be used as therapeutics for viral infections.