We combine confocal imaging, microfluidics, and image analysis to record 3D-images of cells in flow. This enables us to recover the full 3D representation of several hundred living cells per minute. Whereas 3D confocal imaging has thus far been limited to steady specimens, we overcome this restriction and present a method to access the 3D shape of moving objects. The key of our principle is a tilted arrangement of the micro-channel with respect to the focal plane of the microscope. This forces cells to traverse the focal plane in an inclined manner. As a consequence, individual layers of passing cells are recorded, which can then be assembled to obtain the volumetric representation. The full 3D information allows for a detailed comparison with theoretical and numerical predictions unfeasible with, e.g., 2D imaging. Our technique is exemplified by studying flowing red blood cells in a micro-channel reflecting the conditions prevailing in the microvasculature. We observe two very different types of shapes: "croissants" and "slippers." Additionally, we perform 3D numerical simulations of our experiment to confirm the observations. Since 3D confocal imaging of cells in flow has not yet been realized, we see high potential in the field of flow cytometry where cell classification thus far mostly relies on 1D scattering and fluorescence signals.