Haemoglobins from unicellular organisms, plants or animals, share a common structure, which results from the folding, around the heme group, of a polypeptide chain made from 6-8 helices. Nowadays, deciphering the genome of several species allows one to draw the evolutionary tree of this protein going back to 1800 millions of years, at a time when oxygen began to accumulate in the atmosphere. This permits to follow the evolution of the ancestral gene and of its product. It is likely that, only in complex multicellular species, transport and storage of oxygen became the main physiological function of this molecule. In addition, in unicellular organisms and small invertebrates, it is likely that the main function of this protein was to protect the organism from the toxic effect of O2, CO and NO*. The very high oxygen affinity of these molecules, leading them to act rather as a scavenger as an oxygen carrier, supports this hypothesis. Haemoglobins from microorganisms, which may probably be the closest vestiges to the ancestral molecules, are divided into three families. The first one is made from flavohaemoglobins, a group of chimerical proteins carrying a globin domain and an oxido-reduction FAD-dependant domain. The second corresponds to truncated haemoglobins, which are hexacoordinated with very high oxygen-affinity molecules, 20-40 residues shorter than classical haemoglobins. The third group is made from bacterial haemoglobins such as that of Vitreoscilla. Some specific structural arrangements in the region surrounding the heme are cause of their high oxygen affinity. In plants, two types of haemoglobins are present (non-symbiotic and symbiotic), that arose from duplication of an ancestral vegetal gene. Non-symbiotic haemoglobins, which are probably the oldest, are scarcely distributed within tissues having high energetic consumption. Conversely, symbiotic haemoglobins (also named leghaemoglobins) are present at a high concentration (mM) mostly in the rhizomes of legumes, where they are involved in nitrogen metabolism. In some species, haemoglobin was proposed to be an oxygen sensor bringing to the organism information to adjust metabolism or biosynthesis to the oxygen requirement. Elsewhere haemoglobin may act as final electron acceptors in oxido-reduction pathways. Evolution of haemoglobin in invertebrates followed a large variety of scenarios. Some surprising functions as sulphide acquisition in invertebrates living near hydrothermal vents, or a role in the phototrophism of worm need to be mentioned. In invertebrates, the size of haemoglobin varies from monomers to giant molecules associating up to 144 subunits, while in vertebrates it is always a tetramer. In some species, several haemoglobins, with completely different structure and function, may coexist. This demonstrates how hazardous may be to extrapolate the function of a protein from only structural data.