Eukaryotic histone deacetylase 10 (HDAC10) is a Zn2+-dependent hydrolase that exhibits catalytic specificity for the hydrolysis of the polyamine N8-acetylspermidine. The recently determined crystal structure of HDAC10 from Danio rerio (zebrafish) reveals a narrow active site cleft and a negatively charged "gatekeeper" (E274) that favors the binding of the slender cationic substrate. Because HDAC10 expression is upregulated in advanced-stage neuroblastoma and induces autophagy, the selective inhibition of HDAC10 suppresses the autophagic response and renders cancer cells more susceptible to cytotoxic chemotherapeutic drugs. Here, we describe X-ray crystal structures of zebrafish HDAC10 complexed with eight different analogues of N8-acetylspermidine. These analogues contain different Zn2+-binding groups, such as hydroxamate, thiolate, and the tetrahedral gem-diolate resulting from the addition of a Zn2+-bound water molecule to a ketone carbonyl group. Notably, the chemistry that accompanies the binding of ketonic substrate analogues is identical to the chemistry involved in the first step of catalysis, i.e., nucleophilic attack of a Zn2+-bound water molecule at the scissile carbonyl group of N8-acetylspermidine. The most potent inhibitor studied contains a thiolate Zn2+-binding group. These structures reveal interesting geometric changes in the metal coordination polyhedron that accommodate inhibitor binding. Additional interactions in the active site highlight features contributing to substrate specificity. These interactions are likely to contribute to inhibitor binding selectivity and will inform the future design of compounds selective for HDAC10 inhibition.