  In this review I briefly describe the nature of the three kinds of High-Mass
X-ray Binaries (HMXBs), accreting through: (i) Be circumstellar disc, (ii)
supergiant stellar wind, and (iii) Roche lobe filling supergiants. A previously
unknown population of HMXBs hosting supergiant stars has been revealed in the
last years, with multi-wavelength campaigns including high energy (INTEGRAL,
Swift, XMM, Chandra) and optical/infrared (mainly ESO) observations. This
population is divided between obscured supergiant HMXBs, and supergiant fast
X-ray transients (SFXTs), characterized by short and intense X-ray flares. I
discuss the characteristics of these types of supergiant HMXBs, propose a
scenario describing the properties of these high-energy sources, and finally
show how the observations can constrain the accretion models (e.g. clumpy
winds, magneto-centrifugal barrier, transitory accretion disc, etc). Because
they are the likely progenitors of Luminous Blue Variables (LBVs), and also of
double neutron star systems, related to short/hard gamma-ray bursts, the
knowledge of the formation and evolution of this HMXB population is of prime
importance.
