Histone deacetylases (HDACs) catalyze the removal of acetyl groups from acetyl-lysine in histones to promote gene repression. Eukaryotic HDACs are classified into three classes based on sequence homology: class I (yRpd3-like, TSA-sensitive, nuclear), class II (yHda1-like, TSA-sensitive, shuttles between nucleus and cytoplasm), and class III (ySir2-like, NAD-dependent). Recent structural studies of HDACs and their bacterial homologs have provided insights into substrate recognition and catalysis. HDLP, a bacterial homolog of class I/II HDACs, has a compact architecture with a pronounced pocket for acetyl-lysine binding, a bound Zn²⁺ ion, and conserved histidine/aspartic acid residues involved in catalysis. Af1, a bacterial homolog of class III HDACs, in complex with NAD, has a Rossmann fold for NAD binding and distinct sites for acetyl-lysine (site B) and NAD hydrolysis (site C). These structures form a framework for understanding HDAC function, though mechanistic details such as the exact catalytic mechanism and target specificity remain to be addressed.