The phase-field crystal (PFC) model emerged as a convenient approach to describe crystal structures at large (diffusive) timescales through a continuous, periodic order parameter representing the atomic density. It reproduces the main phenomenology for crystalline systems, including solidification and crystal growth, capillarity, lattice deformations as well as nucleation and defect kinematics. The PFC model describes self-consistently anisotropies resulting from the lattice structure and inherently includes elasticity effects. We discuss several extensions of the classical PFC model such as the coupling with thermal transport, enabling the description of a temperature-dependent lattice parameter within a thermodynamically consistent framework. We examine realistic solidification settings in both open as well as closed systems [1]. Then, we discuss in detail the coupling of the PFC model with a macroscopic velocity field, explicitly accounting for the relaxation of elastic excitations. We analyze how this model extension further improves the description of elasticity within the PFC framework, providing deeper insights during complex grain boundary evolution. Specifically, we study direction-dependent mobilities and unidirectional motion of grain boundaries under oscillatory driving forces or cyclic thermal annealing for both bicrystal and polycrystalline microstructures. Consistent with experimental results and molecular dynamics simulations new insights into grain boundary kinetics are provided [2]. REFERENCES [1] Punke M., Wise S. M., Voigt A., Salvalaglio M., A Non-Isothermal Phase-Field Crystal Model with Lattice Expansion: Analysis and Benchmarks. Modelling and Simulation in Materials Science and Engineering, Vol. 33 (2), 2025. [2] Qiu C., Punke M., Tian Y., Han Y., Wang S., Su Y., Salvalaglio M., Pan X., Srolovitz D. J, Han J., Grain boundaries are Brownian ratchets. Science, Vol. 385 (6712), pp. 980-985, 2024.