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.
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