An important feature of naturally self-assembled systems such as leaves and tissues is that they are curved and have embedded fluidic channels that enable the transport of nutrients to, or removal of waste from, specific three-dimensional regions. Here we report the self-assembly of photopatterned polymers, and consequently microfluidic devices, into curved geometries. We discover that differentially photo-crosslinked SU-8 films spontaneously and reversibly curve on film de-solvation and re-solvation. Photolithographic patterning of the SU-8 films enables the self-assembly of cylinders, cubes and bidirectionally folded sheets. We integrate polydimethylsiloxane microfluidic channels with these SU-8 films to self-assemble curved microfluidic networks.