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Features and applications of quasi-spherical settling accretion onto rotatingmagnetized neutron stars in high-mass X-ray binaries are discussed. Thesettling accretion occurs in wind-fed HMXBs when the plasma cooling time islonger than the free-fall time from the gravitational capture radius, which cantake place in low-luminosity HMXBs with $L_x\lesssim 4\times 10^{36}$ erg/s. Webriefly review the implications of the settling accretion, focusing on the SFXTphenomenon, which can be related to instability of the quasi-sphericalconvective shell above the neutron star magnetosphere due to magneticreconnection from fast temporarily magnetized winds from OB-supergiant. If ayoung neutron star in a wind-fed HMXB is rapidly rotating, the propeller regimein a quasi-spherical hot shell occurs. We show that X-ray spectral and temporalproperties of enigmatic $\gamma$ Cas Be-stars are consistent with failedsettling accretion regime onto a propelling neutron star. The subsequentevolutionary stage of $\gamma$ Cas and its analogs should be the X Per-typebinaries comprising low-luminosity slowly rotating X-ray pulsars.

Low-luminosity stellar wind accretion onto neutron stars in HMXBs