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A wreath product is a method to construct an association scheme from twoassociation schemes. We determine the automorphism group of a wreath product.We show a known result that a wreath product is Schurian if and only if bothcomponents are Schurian, which yields large families of non-Schurianassociation schemes and non-Schurian $S$-rings. We also study iterated wreathproducts. Kernel schemes by Martin and Stinson are shown to be iterated wreathproducts of class-one association schemes. The iterated wreath products giveexamples of projective systems of non-Schurian association schemes, with anexplicit description of primitive idempotents.

Wreath products and projective system of non Schurian association schemes