They will eat usually microscopic organisms, although some of the bladderwort species are capable of ingesting newborn fry, etc.
Not a plant you generally want in the same aquarium as fish, shrimp etc.
http://en.wikipedia.org/wiki/Bladderwort#Trapping_mechanismFrances Lloyd devoted several studies to the possibility, often recounted but never previously accounted for under scientific conditions, that Utricularia can consume larger prey such as young tadpoles and mosquito larvae by catching them by the tail, and ingesting them bit by bit.
Prior to Lloyd, several authors had reported this phenomenon and had attempted to explain it by positing that creatures caught by the tail repeatedly set off the trap as they thrash about in an attempt to escape—even as their tails are actively digested by the plant. Lloyd, however, demonstrated that the plant is quite capable of ingestion by stages without the need of multiple stimuli.
Not a plant you generally want in the same aquarium as fish, shrimp etc.