  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 specimen, 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 comparisons 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.
