The properties of structural materials are to a large extent determined by the solid microstructure so that the understanding of the fundamental physics of microstructure formation is critical in the engineering of materials. Also, microstructure selection occurs during the dynamical growth process so that in situ observation of spatio-temporal evolution of the solid–liquid interface shape is necessary. Under terrestrial conditions convection effects dominate in bulk samples, which prevents precise characterization of microstructure selection. Diffusion-controlled experiments in thin samples give microstructures that are neither 2D nor 3D. Rigorous theoretical models using the phase-field method have shown that the fundamental physics of pattern selection in 2D and 3D is significantly different. A benchmark experimental study in bulk samples is thus required under low gravity conditions. In the frame of the joint work of DSIP and MISOL3D projects, respectively, selected by NASA and CNES, microgravity experiments in a model transparent system are planned on ISS using the directional solidification insert (DSI) in the DECLIC facility. The critical aspects of hardware design, the key fundamental issues identified through 1g-experiments, the proposed study on ISS, and the results of rigorous theoretical modeling are presented.