This is the first account of the history of modelling dendritic and cellular solidification. While Part I reviewed the progress up to the year 2000 [Kurz W, Fisher DJ, Trivedi R. Progress in modelling solidification microstructures in metals and alloys: dendrites from 1700 to 2000. Intern Mater Rev. 2019;64:311-354], Part II retraces our modelling capabilities developed during the early years of the present century. Advances in in-situ X-ray observations of solidification of metallic alloys are also presented. While the most important contributions are mentioned, the authors are aware that such a historical review must leave many worthy articles by the wayside. This overview considers dendrite tip growth and morphology, rapid solidification, melt flow, fragmentation, columnar-to-equiaxed transition, dendrite spacings, coalescence, grain competition, and cellular growth. Modelling across the length scales from nano- up to macroscopic solidification phenomena by massive phase field computations or multiscale approaches show the potential for the simulation of real processes such as additive manufacturing, single crystal casting, welding or advanced solidification processes.