We compare two versions of the phase-field theory for polycrystalline solidification, both relying on the concept of orientation fields: one by Kobayashi et al. [Physica D 140 (2000) 141] [15] and the other by Henry et al. [Phys. Rev. B 86 (2012) 054117] [22]. Setting the model parameters so that the grain boundary energies and the time scale of grain growth are comparable in the two models, we first study the grain coarsening process including the limiting grain size distribution, and compare the results to those from experiments on thin films, to the models of Hillert, and Mullins, and to predictions by multiphase-field theories. Next, following earlier work by Granasy et al. [Phys. Rev. Lett. 88 (2002) 206105; Phys. Rev. E 72 (2005) 011605] [17,21], we extend the orientation field to the liquid state, where the orientation field is made to fluctuate in time and space, and employ the model for describing of multi-dendritic solidification, and polycrystalline growth, including the formation of "dizzy" dendrites disordered via the interaction with foreign particles. (C) 2016 Elsevier B.V. All rights reserved.