  Observations with the INTEGRAL satellite have quadrupled the population of
supergiant High Mass X-ray Binaries (HMXBs), revealed a previously hidden
population of obscured supergiant HMXBs, and allowed the discovery of huge and
fast transient flares in supergiant HMXBs. Apart from these 3 observational
facts, has INTEGRAL allowed us to better understand these supergiant HMXBs? Do
we have now a better understanding of the 3 populations of HMXBs, and of their
accretion process, separated in the so-called Corbet diagram? Do we better
apprehend the accretion process in the supergiant HMXBs, and what makes the
fast transient flares so special, in the context of the clumpy wind model, and
of the formation of transient accretion disks? In summary, has the increased
population of supergiant HMXBs allowed a better knowledge of these sources,
compared to the ones that were already known before the launch of INTEGRAL? We
will review all these observational facts, comparing to the current models, to
objectively estimate what is the INTEGRAL legacy on High Mass X-ray Binaries.
