Greenhill is a Senior Research Fellow in the Faculty of Arts and Sciences and Radio Astronomer at the Smithsonian Astrophysical Observatory. His primary research interest in observational cosmology is the Dark Age and Epoch of Reionization.  He also studies topics related to supermassive black holes, accretion disks, and jets. Additional interests include formation mechanisms of high mass stars, masers, radio astronomical instrumentation, interferometry, signal processing, and massively parallel stream supercomputing.