László Gránásy^{1,2}, László Rátkai^{1}, Attila Szállás^{1}, Bálint Korbuly^{1}, Gyula Tóth^{3}, László Környei^{4}, Tamás Pusztai^{1}

^{1}Institute for Solid State Physics and Optics, Wigner Research Centre for Physics, P.O. Box 49, Budapest H-1525, Hungary

^{2}BCAST, Brunel University, Uxbridge, Middlesex, UB8 3PH, United Kingdom

^{3}Department of Mathematical Sciences, Loughborough University, Loughborough, Leicestershire, LE11 3TU, U.K.

^{4}Department of Mathematics and Computational Sciences, Széchenyi István University, Győr 9026, Hungary

Advances in the orientation-field-based phase-field (PF) models made in the past are reviewed. The models applied incorporate homogeneous and heterogeneous nucleation of growth centers and several mechanisms to form new grains at the perimeter of growing crystals, a phenomenon termed growth front nucleation. Examples for PF modeling of such complex polycrystalline structures are shown as impinging symmetric dendrites, polycrystalline growth forms (ranging from disordered dendrites to spherulitic patterns), and various eutectic structures, including spiraling two-phase dendrites. Simulations exploring possible control of solidification patterns in thin films via external fields, confined geometry, particle additives, scratching/piercing the films, etc. are also displayed. Advantages, problems, and possible solutions associated with quantitative PF simulations are discussed briefly.