Models of crystal growth have been defined by comparing macroscopic growth kinetics with theoretical predictions for various growth mechanisms [1,2].The classic Burton-Cabrera-Frank (BCF) theory  predicts that spiral growth at screw dislocations will dominate near equilibrium. Although this has often been observed [2,4], such growth is sometimes inhibited [4,5], which has been assumed to be due to the presence of impurities . At higher supersaturations, growth is commonly modelled by two-dimensional nucleation on the pre-existing surface according to the 'birth and spread' model . In general, the morphology of a growing crystal is determined by the rate of growth of different crystallographic faces, and periodic-bond-chain (PBC) theory [8,9] relates this morphology to the existence of chains of strongly bonded ions in the structure. Here we report tests of such models for the growth of barite crystals, using a combination of in situ observations of growth mechanisms at molecular resolution with the atomic force microscope [10,11] and computer simulations of the surface attachment of growth units. We observe strongly anisotropic growth of two-dimensional nuclei with morphologies controlled by the underlying crystal structure, as well as structure-induced self-inhibition of spiral growth. Our results reveal the limitations of both the BCF and PBC theories in providing a general description of crystal growth.