A phase field theory of crystal nucleation and polycrystalline growth is presented. The model is tested for crystal nucleation in the hard-sphere system. It will be shown that evaluating the model parameters from molecular dynamics simulations, the phase field theory predicts the nucleation barrier accurately. Results of extensive simulations will be presented on transformation kinetics, particle-induced disorder ("dizzy" dendrites), and on the formation of various polycystalline structures, including spherulites. It will be shown that a broad variety of complex solidification morphologies can be recovered by changing only a few model parameters. Finally, heterogeneous crystal nucleation on foreign particles and walls, and solidification in confined volumes (channels, porous medium) will be addressed.

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