Antiviral therapy for human cytomegalovirus (HCMV) currently relies upon direct-acting antiviral drugs. However, it is now well known that these drugs have shortcomings, which limit their use. Here I review the identification and investigation of compounds targeting cellular proteins that have anti-HCMV activity and could supersede those anti-HCMV drugs currently in use. This includes discussion of drug repurposing, for example the use of artemisinin compounds, and discussion of new directions to identify compounds that target cellular factors in HCMV-infected cells, for example screening of kinase inhibitors. In addition, I highlight developing areas such as the use of machine learning and emphasize how interaction with fields outside virology will be critical for development of anti-HCMV compounds.