It is now 30 years since the first report of a potent zinc-dependent histone deacetylase (HDAC) inhibitor appeared. Since then, five HDAC inhibitors have received regulatory approval for cancer chemotherapy while many others are in clinical development for oncology as well as other therapeutic indications. This Perspective reviews the biological and medicinal chemistry advances over the past 3 decades with an emphasis on the design of selective inhibitors that discriminate between the 11 human HDAC isoforms.