The main thrust of this article is to draw together the salient features relevant to understanding the nature of catalysis in acyl‐group transfer. In doing so, an attempt is made to identify common elements of catalysis across diverse acylation processes involving both Lewis and Brønsted acids. Acyl‐group transfer to carbon‐based substrates is the most synthetically useful implementation of this reaction and, as such substrates are frequently moderate nucleophiles, catalysis is most required in acylation of these materials. Procedures and processes aimed at cleaner, more atom‐efficient Friedel–Crafts acylation chemistry are also covered, as are other acylation reactions: these include use of organometallic species and catalysis of acyl‐group transfer to heteroatoms such as O and N in instances where chemo‐ and enantioselective control is important.