Polypterus is a genus of freshwater fish in the bichir family (Polypteridae) of order Polypteriformes. The type species is the Nile bichir (P. bichir). Fishes in this genus live in various areas in Africa. The etymology of the genus name derives from a combination of the Greek prefix πολυ-, poly- (many) and the root word πτερον, pteron (wing or fin) – "many fins". Polypterus is the only known vertebrate to have lungs, but no trachea.
Polypterus was discovered, described, and named in 1802 by Étienne Geoffroy Saint-Hilaire. It is a genus of 10 green to yellow-brown species. Naturalists were unsure whether to regard it as a fish or an amphibian. If it were a fish, what type was it: bony, cartilaginous, or lungfish? 
Some regarded Polypterus as a living fossil, part of the missing link between fishes and amphibians, helping to show how fish fins had evolved to become paired limbs.
In 1861, Thomas Huxley created the order Crossopterygii to house animals, fossil and living, that possessed lungs and fleshy pectoral fins with lobes. He placed Polypterus and Calamoichthys within this order, allocating them to a new tribe, Polypterini, which he created especially for them. The weight of Huxley’s authority allowed this allocation to last in textbooks and lectures long after it had been disproved.
In the 1870s and 1880s, Francis Balfour and his students had shown that embryology could help to answer questions about the evolution of species. No one had studied the embryology of Polypterus. Someone who could do this might prove the “missing link” theory and be greatly honoured, but it could be a dangerous quest. The only breeding Polypterus specimens were in swampy parts of African rivers. Africa was a turbulent place and swamps were rich breeding grounds for mosquitoes carrying malaria.
Two men, Nathan Harrington and John Samuel Budgett, attempted to answer this question by making repeated expeditions to Africa. Harrington failed on his first attempt in 1898 and died early on his second in 1899 before he could reach his destination. Budgett failed in 1898/9, 1900, and 1902. He finally succeeded in 1903, but died of blackwater fever shortly after his return to England. He left excellent samples and drawings, but his only writing was a diary. Consequently, his results on Polypterus were written up and published by his friend John Graham Kerr.
Drawing on this work, in 1907, E.S.Goodrich reported to the British Association the then current state of evidence 'against' Polypterus being a crossopterygian, placing it within the palaeoniscids, the most primitive actinopterygians. 
Much later, in 1946, Romer, confirmed this view, but he also wrote,"The weight of Huxley's  opinion is a heavy one, and even today many a text continues to cite Polypterus as a crossopterygian and it is so described in many a classroom, although students of fish evolution have realized the falsity of this position for many years.... Polypterus...is not a crossopterygian, but an actinopterygian, and hence can tell us nothing about crossopterygian anatomy and embryology." .
Hall (2001), relying on Patterson (1982) and Noack et al. (1996), writes, "Phylogenetic analyses using both morphological and molecular data affirm Polypterus as a living stem actinopterygian." Research is ongoing. Most of the conclusions drawn by Kerr from Budgett’s specimens have been confirmed, but many questions remain.
Polypterus have rarely been bred in captivity. The first success was that of Polypterus senegalus by Arnoult in 1964, a species spawned repeatedly since (see Hartl, 1981; Bartsch and Gemballa, 1992; Bartsch et al., 1997 and Schugardt, 1997).
Shortly after Arnoult’s success, a second species, Polypterus ornatipinnis, was spawned by Armbrust for the first time (1966 and 1973) and bred subsequently by Azuma in 1986; Wolf, 1992; Bartsch and Britz, 1996. The third species successfully spawned in captivity was Polypterus endlicheri by Azuma in 1995.
Zoo Basel have been successful in breeding Polypterus in captivity. In December 2005, several eggs were laid, and at the beginning of 2006, six young had hatched. Within two months, they reached 10 cm (about 4 in). 
In 2014 Researchers at McGill University published in the journal Nature, turned to a living fish, called Polypterus, to help show what might have happened when fish first attempted to walk out of the water. The team of researchers raised juvenile Polypterus on land for nearly a year, with an aim to revealing how these 'terrestrialized' fish looked and moved differently.  VIDEO: 
- Polypterus ansorgii Boulenger, 1910 (Guinean bichir)
- Polypterus bichir Lacépède, 1803
- Polypterus delhezi Boulenger, 1899 (Barred bichir)
- Polypterus endlicheri Heckel, 1847
- P. e. congicus Boulenger, 1898 (Congo bichir)
- P. e. endlicheri Heckel, 1847 (Saddled bichir)
- Polypterus mokelembembe Schliewen & Schäfer, 2006 (Mokèlé-mbèmbé bichir)
- Polypterus ornatipinnis Boulenger, 1902 (Ornate bichir)
- Polypterus palmas Ayres, 1850
- P. p. buettikoferi Steindachner, 1891 (Buettikofer's bichir)
- P. p. palmas Ayres, 1850 (Shortfin bichir)
- P. p. polli J. P. Gosse, 1988 (Poll's bichir)
- Polypterus retropinnis Vaillant, 1899 (West African bichir)
- Polypterus senegalus Cuvier, 1829 (Gray bichir)
- P. s. meridionalis Poll, 1941
- P. s. senegalus Cuvier, 1829
- Polypterus teugelsi Britz, 2004 (Cross River bichir)
- Polypterus weeksii Boulenger, 1898 (Mottled bichir)
- Hall (2001)
- Kerr, J.G. (1907)
- Goodrich (1908)
- Romer(1946), pp. 60-61), quoted by Hall
Goodrich, E. S. (1908). On the systematic position of Polypterus. Report of the 77th Meeting of the British Association for the Advancement of Science (1907): 545-546. Quoted by Hall
Hall, B. K. (2001) John Samuel Budgett (1872-1904): In Pursuit of Polypterus, BioScience, Vol. 51, No. 5 (May, 2001), pp. 399-407
Kerr, J.G. (1907), The development of Polypterus senegalus Cuv., Pages 195-290 in Kerr, J.G., (ed. 1907), The Work of John Samuel Budgett, Balfour Student of the University of Cambridge: Being a Collection of His Zoological Papers, together with a Biographical Sketch by A . E. Shipley, F.R.S., and Contributions by Richard Assheton, Edward J.Bles, Edward T. Browne, J. Herbert Budgett and J. Graham Kerr. Cambridge (UK): Cambridge University Press.
Noack K, Zardoya R, Meyer A. 1996. The complete mitochondrial DNA sequence of the bichir (Polypterusor natipinnis), a basal ray-finned fish: Ancient establishment of the consensus vertebrate gene order. Genetics 144:1165-1180, cited by Hall
Patterson C. (1982). Morphology and interrelationships of primitive actinopterygian fishes. American Zoologist 22: 241-260, cited by Hall.
Romer, A S. (1946). The early evolution of fishes, Quarterly Review of Biology 21: 33-69, cited by Hall