Methods of inhibiting replication of human cytomegalovirus (HCMV) are disclosed. In various configurations, these methods comprise administering a therapeutically effective amount of a bromodomain inhibitor to a subject in need thereof. Bromodomain inhibitors including methyltriazolodiazepine-related compounds, 3,5-dimethylisoxazole-related compounds, 3-methyldihydroquinazolinone-related compounds, N-acetyl-2-methyltetrahydroquinoline-related compounds, quinazolone-related compounds, diazobenzene-related compounds, and triazolopyridazine-related compounds can be used to inhibit viral replication.