Over the past forty years, the series of MCWASP conferences has been the witness of the fantastic developments in the field of modeling of welding and solidification processes. This has been made possible thanks to the exponential increase in computing power but also to the emergence of new numerical methods and tools. While the "size" of computer simulations reported in MCWASP proceedings continues to follow Moore's law describing the evolution of computers power, the present contribution focuses on the evolution of microstructure modeling. In this respect, a major turning point is the introduction of the phase field (PF) method in the mid-90's. While PF is still the method of choice for the direct simulation of microstructure formation, it is also very CPU intensive. Therefore, it did not replace and rather complement other coarser methods such as analytical micro-macro models, Cellular Automata coupled with Finite Elements (so-called CAFE approach), modified-CAFE methods, mesoscopic model based on a dendrite envelope or Dendritic Needle Network (DNN) model. Some of these models as well as PF are coupled with fluid flow models based either on standard Navier-Stokes or Lattice-Boltzmann solutions. In parallel to these developments, wonderful experimental tools have become available to complement and validate numerical simulations: in situ X-ray radiography and tomography, EBSD, atom probe, FIB, etc. Besides a review of the past forty years, the present contribution will outline future directions of research in the area of microstructure modeling.