Open microfluidic cell culturing devices offer new possibilities to simplify loading, culturing, and harvesting of individual cells or microtissues due to the fact that liquids and cells/microtissues are directly accessible. We present a complete workflow for microfluidic handling and culturing of individual cells and microtissue spheroids, which is based on the hanging-drop network concept: The open microfluidic devices are seamlessly combined with fluorescence-activated cell sorting (FACS), so that individual cells, including stem cells, can be directly sorted into specified culturing compartments in a fully automated way and at high accuracy. Moreover, already assembled microtissue spheroids can be loaded into the microfluidic structures by using a conventional pipet. Cell and microtissue culturing is then performed in hanging drops under controlled perfusion. On-chip drop size control measures were applied to stabilize the system. Cells and microtissue spheroids can be retrieved from the chip by using a parallelized transfer method. The presented methodology holds great promise for combinatorial screening of stem-cell and multicellular-spheroid cultures.