The phase-field method has recently emerged as the most powerful computational tool for simulating complicated dendrite growth. However, these simulations are still limited to two-dimensional or small three-dimensional spaces; therefore, to realistic and practical dendritic structures, it is crucial to develop a large-scale phase-field simulation technique. This review discusses the phase-field modeling and simulations of dendrite growth from the fundamental model to cutting-edge very-large-scale simulations. First, phase-field models for the dendrite growth of pure materials and binary alloys and their histories are summarized. Then, models and studies of interface anisotropy, polycrystalline solidification, and solidification with convection, which are very important in dendritic solidification, are reviewed. Finally, by introducing very-large-scale phase-field simulations performed recently using a graphics processing unit supercomputer, the power, potential and importance of the very-large-scale phase-field simulation are emphasized.