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During casting often a dendritic microstructure is formed, resulting in a columnar or equiaxed grain structure, or leading to a transition from columnar to equiaxed growth (CET). Especially the detailed knowledge of the critical parameters for CET is important, because the microstructure determines significantly the materials properties. To provide unique data for testing of fundamental theories of grain and microstructure formation, solidification experiments in microgravity environment were performed within the ESA MAP project CETSOL. Reduced gravity allows for pure diffusive solidification conditions, i.e., suppressing melt flow and sedimentation and floatation effects. On-board the International Space Station ISS Al-7wt%Si alloys with and without grain refiners were solidified in different temperature gradients and with different cooling conditions. Detailed analysis of the microstructure and the grain structure showed columnar growth in case of non-refined alloy. CET was detected 2 only for refined alloys, either as a sharp CET in case of a sudden increase of the solidification velocity, or as a progressive CET in case of a continuous decrease of the temperature gradient. The unique experimental data were used for numerical modelling of CET with three different approaches: (i) a front tracking model using an equiaxed growth model, (ii) a 3D CAFE model, (iii) a 3D dendrite needle network (DNN) method. Each model allows predicting the columnar dendrite tip undercooling and the growth rate with respect time. Furthermore, the positions of CET and the spatial extent of the CET, being sharp or progressive, are in reasonably good quantitative agreement with experimental measurements.