The quantitative phase-field simulations were reviewed on the processes of solidification of pure metals and alloys.The quantitative phase-field equations were treated in a diffuse thin-interface limit,which enabled the quantitative links between interface dynamics and model parameters in the quasi-equilibrium simulations.As a result,the quantitative modeling is more effective in dealing with microstructural pattern formation in the large scale simulations without any spurious kinetic effects.The development of the quantitative phase-field models in modeling the formation of microstructures such as dendritic structures,eutectic lamellas,seaweed morphologies,and grain boundaries in different solidified conditions was also reviewed with the purpose of guiding to find the new prospect of applications in the quantitative phase-field simulations. The quantitative phase-field simulations were reviewed on the processes of solidification of pure metals and alloys. The quantitative phase-field equations were treated in a diffuse thin-interface limit, which enabled the quantitative links between interface dynamics and model parameters in the quasi- equilibrium simulations. As a result, the quantitative modeling is more effective in dealing with microstructural pattern formation in the large scale simulations without any spurious kinetic effects. The development of the quantitative phase-field models in modeling the formation of microstructures such as dendritic structures, eutectic lamellas, seaweed morphologies, and grain boundaries in different solidified conditions was also reviewed with the purpose of guiding to find the new prospect of applications in the quantitative phase-field simulations.