Abstract | We consider coupled chemotaxis-fluid models aimed to describe swimming bacteria, which are able exert bio-convective flow patterns on length scales much larger than the bacteria size. When looking at the microorganisms in detail, experimentalists have observed that high concentration of swimming microorganisms show collective behaviour, in the sense that each organism aligns its swimming direction with those of its neighbours. We discuss different PDE models for the phenomena, give results and challenges in analysing them. |