Stellar wind accretion in high-mass X-ray binaries

Recent discoveries have confirmed the existence of a large population of X-ray sources fuelled by accretion from the stellar wind of an OB supergiant. Such systems are powerful laboratories to study many aspects of astrophysics. Over the last decades, the physics of accretion in these systems has been the subject of extensive research, mainly through numerical methods. In spite of this effort, large uncertainties remain in our understanding, reflecting the complexity of the physical situation. A crucial issue that remains open is the possible formation of accretion discs. Though the spin evolution of neutron stars in these systems suggests that angular momentum is, at least occasionally, accreted, and many observational facts seem to require the existence of discs, computational results do not favour this possibility. In this brief review, I will summarise some of the open questions in this area.