Anaerobic ammonium-oxidizing (anammox) bacteria primarily grow by the oxidation of ammonium coupled to nitrite reduction, using CO2 as the sole carbon source. Although they were neglected for a long time, anammox bacteria are encountered in an enormous species (micro)diversity in virtually any anoxic environment that contains fixed nitrogen. It has even been estimated that about 50% of all nitrogen gas released into the atmosphere is made by these ‘impossible’ bacteria. Anammox catabolism most likely resides in a special cell organelle, the anammoxosome, which is surrounded by highly unusual ladder-like (ladderane) lipids. Ammonium oxidation and nitrite reduction proceed in a cyclic electron flow through two intermediates, hydrazine and nitric oxide, resulting in the generation of proton-motive force for ATP synthesis. Reduction reactions associated with CO2 fixation drain lectrons from this cycle, and they are replenished by the oxidation of nitrite to nitrate. Besides ammonium or nitrite, anammox bacteria use a broad range of organic and inorganic compounds as electron donors. An analysis of the metabolic opportunities even suggests alternative chemolithotrophic lifestyles that are independent of these compounds. We note that current concepts are still largely hypothetical and put forward the most intriguing questions that need experimental answers.