Powered flight has evolved three times in the vertebrates: in the birds, the bats and the extinct pterosaurs. The largest bats ever known are at least an order of magnitude smaller than the largest members of the other two groups. Recently it was argued that different scaling of wingbeat frequencies to body mass in birds and bats can help explain why the largest birds are larger than the largest bats. Here I extend this argument in two ways. Firstly, I suggest that different respiratory physiologies are key to understanding the restriction on bat maximum size compared to birds. Secondly, I argue that a respiratory physiology similar to birds would have been a prerequisite for the gigantism seen in pterosaurs.