Acetylation of lysine residues is an important post-translational modification. In humans there are large number of acetylation sites in the proteome, with 5-10% of proteins being acetylated. The acetylation status of these sites is tightly regulated and reversible, with histone deacetylase enzymes performing the deacetylation reaction. In humans there are 4 classes of HDACs, with Class I, II and IV consisting of 11 Zn2+ dependent enzymes. Currently there are 4 FDA-approved HDAC inhibitors that target hematological malignancies. However these inhibitors are not isozyme selective and thus have significant off target effects resulting in significant side effects. There is scope for creating isozyme specific inhibitors through manipulation of the Zn2+ binding group, the linker region and/or the capping group. This thesis focuses on structural characterization of variations in these three inhibitor components for the design of HDAC6 selective inhibitors that specifically target the second catalytic domain of HDAC6. This domain functions as a tubulin and tau deacetylase making it a target for disease therapy. Difluoromethyl-1,3,4-oxidazoles were investigated as an alternative Zn2+ binding group. These inhibitors are highly selective for HDAC6, and it was determined that they are mechanism-based inhibitors that are tight binding and irreversible due to the ring opening reaction that generates a Zn2+-bound diacylhydrazide. In the linker region, fluorination of capless benzyl hydroxamates shows that a meta difluoro substitution pattern yields a preference for HDAC6 binding and selectivity. Finally to explore the functional consequences of variations in the capping group, structural characterization of macrocyclic peptide inhibitors provided insight into short-range protein interactions that can occur between capping groups and the outer active site of HDAC6. Outside of the human HDACs, Zn2+-dependent HDACs are found in a large number of organisms, including bacteria. This thesis also describes structure-function relationships for a Class II Zn2+-dependent deacetylase from the multidrug-resistant Gram-negative species Acinetobacter baumannii. This work sets the stage for the investigation of prokaryotic HDACs as potential drug targets for antibacterial therapy.