Representation theory studies ways to represent algebraic objects (such as associative algebras) as algebras of linear operators on vector spaces. Physics has a long record of supplying interesting algebras to study. In my talk I will consider algebras that arise as quantizations of moduli spaces of instantons. I will review known results about representations of these algebras, mention their relevance to Physics, and, time permitting, outline some prospective developments: representations over fields of positive characteric are coming!