The 61Ni ( alpha ,n gamma ) 64Zn reaction has been studied 8.6 MeV and 9.35 MeV bombarding energies together with the 56Fe(11B, p2n gamma )64Zn reaction at 30 MeV bombarding energy. The gamma -ray decay scheme of 64Zn has been deduced up to 5.7 MeV excitation by means of gamma - gamma coincidence experiments and n- gamma coincidence experiments. Spins and parities have been deduced for most of the high-spin states between 3.1 and 5.7 MeV excitation by means of gamma -ray angular distribution measurements together with gamma -ray linear polarisation measurements. The lifetimes of levels have been measured by DSAM enabling electromagnetic transition rates to be determined for many transitions. The results have been compared with shell-model, cluster-vibration model and interacting boson approximation calculations.