Since the COVID-19 pandemic swept across the globe, researchers have been trying to understand its origin, life cycle, and pathogenesis. There is a striking variability in the phenotypic response to infection with SARS-CoV-2 that may reflect differences in host genetics and/or immune response. It is known that the human epigenome is influenced by ethnicity, age, lifestyle, and environmental factors, including previous viral infections. This Review examines the influence of viruses on the host epigenome. We describe general lessons and methodologies that can be used to understand how the virus evades the host immune response. We consider how variation in the epigenome may contribute to heterogeneity in the response to SARS-CoV-2 and may identify a precision medicine approach to treatment.