Hydroxamate‐based histone deacetylase inhibitors (HDACIs) have been approved as therapeutic agents by the US Food and Drug Administration for use in oncology applications. While the potential utility of such HDACIs in other areas of medicinal chemistry is tremendous, there are significant concerns that “pan‐HDAC inhibitors” may be too broadly acting and/or toxic for clinical use beyond oncology. In addition to the isozyme selectivity challenge, the potential mutagenicity of hydroxamate‐containing HDAC inhibitors represents a major hindrance in their application to other therapeutic areas. Herein we report on the mutagenicity of known hydroxamates, discuss the mechanisms responsible for their genotoxicity, and review some of the current alternatives to hydroxamates. We conclude that the hydroxamate group, while providing high‐potency HDACIs, is not necessarily the best zinc‐binding group for HDACI drug discovery.