We will discuss the (profinite) iterated monodromy groups (pfIMGs) of unicritical polynomials. It can be shown that the geometric pfIMGs have a set of generators satisfying certain explicit wreath recursions that depend only on the structure of the critical orbit and an integer mod d. These generalize Richard Pink’s descriptions in the case of quadratic PCF polynomials, which are always unicritical. With these descriptions, one can describe or bound the outer Galois action of the arithmetic pfIMG on the geometric pfIMG, also generalizing Pink’s work. This action determines the constant field extension associated to the arboreal extension: it contains infinitely many roots of unity in the periodic case and finitely many, bounded by (d) or better, in all but one but one preperiodic polynomial of each degree; partial progress suggests the remaining family will have infinitely many roots of unity, unlike the other preperiodic cases. This is joint work with Trevor Hyde.