Measurements of the five most significant angular coefficients, A0 through A4, for Z bosons produced in pp collisions at s=8TeV and decaying to μ+μ− are presented as a function of the transverse momentum and rapidity of the Z boson. The integrated luminosity of the dataset collected with the CMS detector at the LHC corresponds to 19.7fb−1. These measurements provide comprehensive information about the Z boson production mechanisms, and are compared to the QCD predictions at leading order, next-to-leading order, and next-to-next-to-leading order in perturbation theory.