Abstract: I will give a quick overview of twisted Kloosterman sums and their associated sheaves defined by Deligne--Katz. Then I will talk about matrix Kloosterman sums defined by Erdélyi--Tóth and about my recent work that reduces these to classical Kloosterman sums and Hall--Littlewood polynomials. In both parts of the talk, I will explain a relation between exterior/symmetric powers of the Kloosterman sheaf and a special value of a Bessel function of a representation of GLn(Fq).