This is a report on research under the aegis of NASA on a collaboration between ESA and NASA for solidification experiments on the International Space Station (ISS). The focus has been on the effect of convection on the microstructural evolution in the directional solidification (DS) of alloys, including experiments, in which Al-7 wt.% Si is the subject alloy, have been carried out under well-defined processing conditions. By comparing the microstructures in terrestrially-processed samples and ISS-processed samples, we have observed that the primary dendrite arm spacings of two samples grown in the low-gravity environment of the ISS show good agreement with a dendrite-growth model based on diffusion controlled growth. The gravity driven convection (i.e., thermosolutal convection) in terrestrially grown samples has the effect of decreasing the primary dendrite arm spacings and causes macrosgregation. In order to process DS-samples aboard the ISS, dendritic-seed crystals have to partially remelted in a stationary thermal gradient before the DS is carried out. Microstructural changes and macrosegregation effects during this period are described.