Histone deacetylases are set of enzymes that have been of interest in drug discovery for the last more than 3 decades. They are responsible for cleaving of acetyl groups from acetyl-lysine residues in histones and various non-histone proteins. Histone deacetylase inhibition is a contemporary, clinically validated therapeutic tactic for cancer treatment. Hydroxamic acid derivatives are among the first compounds to be identified as histone deacetylase inhibitors, comprising of three structural units namely, the surface recognition domain generally a hydrophobic group, linker domain consist of linear or cyclic structures and zinc binding group. In the present review, we are focusing on vital aspects of histone deacetylases, their classification and importance of hydroxamic acid based histone deacetylase inhibitor as anticancer agent.