We report the stable and low energy metastable structures of zinc oxide clusters, (ZnO)n, n = 1−32, found using an evolutionary algorithm with polarizable shell interatomic potentials. This study comprises the first systematic search for nanoparticulate structures for this compound above n = 18 and includes a comparison with other recent studies. As a function of n, global minimum and low energy metastable clusters evolve from rings (up to ca. 0.8 nm in diameter) to perfect closed bubbles (up to ca. 1.2 nm in diameter in the range reported), which are the structures that only contain tetragonal and hexagonal faces and all ions have a coordination number of three. The transition between the two structural families is blurred, with key structures that are also (i) open bubbles, which contain octagonal or larger faces, and (ii) bubbles that have handles, or two-dimensional ring fragments attached. A new nomenclature to describe these structures is defined. We find a greater stability of tetrahedral and trigonal coordinations compared to tetragonal for ZnO clusters in the range considered. Of the predicted global minimum clusters, spheroid cages n = 12, 16, and 28, with symmetry point groups Th, Td and T, and barrels, which are a common motif, exhibit a relatively high stability. Bulklike wurtzite, or multilayered clusters, as well as the simple cuboid and related rock salt configurations are not found to be thermodynamically stable in the size range considered.