We give a detailed account of Deligne’s letter [13] to Drinfeld dated June 18, 2011, in which he shows that there are finitely many irreducible lisse $\overline{\mathbb Q}_{\ell}$-sheaves with bounded ramification, up to isomorphism and up to twist, on a smooth variety defined over a finite field. The proof relies on Lafforgue’s Langlands correspondence over curves [27]. In addition, Deligne shows the existence of affine moduli of finite type over $\mathbb Q$. A corollary of Deligne’s finiteness theorem is the existence of a number field which contains all traces of the Frobenii at closed points, which was the main result of [12] and which answers positively his own conjecture [9, Conj. 1.2.10 (ii)].