Defined by Haiman, wreath Macdonald polynomials are generalizations of the well-known Macdonald polynomials to wreath products of cyclic groups with symmetric groups. For a fixed cylic group Z/rZ, these can be viewed as partially-symmetric polynomials, where there are r families of symmetric variables. Many results for the usual Macdonald polynomials should have analogues in the wreath setting: e.g. Macdonald operators, bispectral duality, evaluation formulas, and norm formulas. Precise conjectures for these analogues can be tricky to write down and even more difficult to prove. A guiding principle is that various quantum algebraic methods in the classical Macdonald theory should have generalizations in the wreath setting. I will present work, joint with Daniel Orr and Mark Shimozono, that studies these polynomials via the rank r quantum toroidal algebra.