Sirtuins are NAD(+)-dependent enzymes universally present in all organisms, where they play central roles in regulating numerous biological processes. Although early studies showed that sirtuins deacetylated lysines in a reaction that consumes NAD(+), more recent studies have revealed that these enzymes can remove a variety of acyl-lysine modifications. The specificities for varied acyl modifications may thus underlie the distinct roles of the different sirtuins within a given organism. Additional contributions to sirtuin function may also result from structural variations both within and flanking the conserved catalytic domain. This review summarizes the structure, chemistry, and substrate specificity of sirtuins with a focus on how different sirtuins recognize distinct substrates and thus carry out specific functions. Expected final online publication date for the Annual Review of Biochemistry Volume 85 is June 02, 2016. Please see http://www.annualreviews.org/catalog/pubdates.aspx for revised estimates.