Defined by Haiman, the wreath Macdonald polynomials are a generalization of the modified Macdonald polynomials where the symmetric groups are replaced by their wreath products with a fixed cyclic group. Through a wreath analogue of the Frobenius characteristic, they correspond to partially-symmetric functions. Their existence and Schur positivity were proved by Bezrukavnikov--Finkelberg using geometric methods, and many of their combinatorial aspects remain unexplored. In this talk, I will introduce them from a symmetric-function-theoretic perspective, building up to a conjectural wreath generalization of the plethystic formula of Garsia--Haiman--Tesler (GHT). If time permits, I will discuss the interplay with quantum toroidal algebras, both in the original GHT formula and in the wreath setting.