The nature of dark matter is one of the big open problems in science. Ultralight bosons in Bose-Einstein condensates (BECs) have become prominent candidates for dark matter. Exemplifying quantum phenomena on top of being (self-)gravitating, its dynamics differs from standard cold dark matter, whether it be the appearance of solitons or quantized vortices in galactic halos, or the formation route of cosmic structures, in general. Many predictions have been already compared to astronomical observations. In this talk, I will focus on important similarities and differences to dilute laboratory BECs, in light of the more complicated set of equations of motion, notably the Gross-Pitaevskii-Poisson system. Some of this will be exemplified by quantized vortices in rotating dark matter halos. Finally, I will highlight open questions related to the rigorous analysis of gravitating BECs.