Reversible lysine acetylation serves as a critical regulatory pathway for diverse cellular processes. As a result, the dysregulation of proteinaceous acetyl-L-lysine hydrolysis is connected to severe medical conditions including neurological disorders, immune dysfunction, and cancer. Inhibition of the enzymes responsible for catalyzing this reaction, histone deacetylases (HDACs), has demonstrated promising results as a route to clinical intervention in many of these diseases. Of the 18 known HDACs, 11 are metal-dependent enzymes that have similar mechanisms and each regulates the function of numerous protein substrates in vivo. This frustrates the design of small molecules targeting a single isozyme, meaning that modern FDA-approved HDAC inhibitors exhibit various side effects that make them less-than-optimal for broad clinical application. This thesis describes the characterization of HDAC–inhibitor complexes by crystallography, supported by thermodynamic and enzymological measurements, focusing on a class I enzyme, HDAC8, and a class IIb enzyme, HDAC6. Structural analysis of complexes with inhibitors exhibiting class- or isozyme-selective activity has illuminated the structural underpinnings of isozyme-selective HDAC inhibition. For instance, irreversible inhibition of class I HDACs by the epoxyketone-based inhibitor trapoxin A is due to the conformation of the epoxide group, rather than a long-presumed covalent modification in the active site. With regard to HDAC6, selective hydroxamates exhibit an unusual monodentate metal-coordination mode mediated by steric interactions at the protein surface. HDAC6 is also predisposed to be inhibited by hydroxamates over other isozymes due to a unique entropic gain associated with inhibitor binding. Finally, mercaptoacetamides serve as an alternative, non-genotoxic zinc-binding group that can exploit subtle mechanistic differences between isozymes. Taken together, these studies have constructed a framework for the design of selective HDAC inhibitors for better-targeted therapeutics.