The complexity of blood flows is an intense subject of research since the pioneering works of Poiseuille and through studies over a wide range of scales, from the single red blood cell to dense suspensions in capillary networks, using a large variety of techniques. The subtle effects that are responsible for the structure of blood flows in vessels can benefit from the use of microgravity platforms in order to suppress sedimentation that prevents precise measurements of red blood cell dynamics. The BIOMICS experiment was performed in the MASER11 and MASER12 sounding rockets and was preceded and followed by several parabolic flight experiments in which two important phenomena were investigated using red blood cells and biomimetic model systems like lipid vesicles: the lift forces that push red blood cells away from walls and hydrodynamic interactions between cells that contribute to spreading, mixing, and segregation of different cell types. Parabolic flights played a crucial role in the definition of the scientific questions, preliminary experiments, hardware development and testing, as well as the definition of protocols , and were central in an experimental program combining ground and flight experiments on different platforms.