Human cytomegalovirus (HCMV) is a ubiquitous betaherpesvirus that frequently causes morbidity and mortality in individuals with insufficient immunity, such as transplant recipients, AIDS patients, and congenitally infected newborns. Several antiviral drugs are approved to treat HCMV infections. However, resistant HCMV mutants can arise in patients receiving long-term therapy. Additionally, side effects and the risk to cause birth defects limit the use of currently approved antivirals against HCMV. Therefore, the identification of new drug targets is of clinical relevance. Recent work identified DNA-damage binding protein 1 (DDB1) and the family of the cellular cullin (Cul) RING ubiquitin (Ub) ligases (CRLs) as host-derived factors that are relevant for the replication of human and mouse cytomegaloviruses. The first-in-class CRL inhibitory compound Pevonedistat (also called MLN4924) is currently under investigation as an anti-tumor drug in several clinical trials. Cytomegaloviruses exploit CRLs to regulate the abundance of viral proteins, and to induce the proteasomal degradation of host restriction factors involved in innate and intrinsic immunity. Accordingly, pharmacological blockade of CRL activity diminishes viral replication in cell culture. In this review, we summarize the current knowledge concerning the relevance of DDB1 and CRLs during cytomegalovirus replication and discuss chances and drawbacks of CRL inhibitory drugs as potential antiviral treatment against HCMV.