Quasi-spherical subsonic accretion can be realized in slowly rotating wind-fed X-ray pulsars (XPSRs) at X-ray luminosities <4 10^{36} erg/s. In this regime the accreting matter settles down subsonically onto the rotating magnetosphere, forming an extended quasi-static shell. The shell mediates the angular momentum removal from the rotating NS magnetosphere by shear turbulent viscosity in the boundary layer or via large-scale convective motions. In the last case the differential rotation law in the shell is close to iso-angular-momentum rotation. The accretion rate through the shell is determined by the ability of the plasma to enter the magnetosphere due to Rayleigh-Taylor instabilities while taking cooling into account. Measurements of spin-up/spin-down rates of quasi-spherically wind accreting XPSRs in equilibrium with known orbital periods (like e.g. GX 301-2 and Vela X-1) enable determination of the main dimensionless parameters of the model and the NS magnetic field. For equilibrium pulsars with independent measurements of the magnetic field, the stellar wind velocity from the companion can be estimated without the use of complicated spectroscopic measurements. For non-equilibrium pulsars, a maximum possible spin-down torque exerted on the accreting NS exists. From observations of the spin-down rate and X-ray luminosity in such pulsars (GX 1+4, SXP 1062, 4U 2206+54, etc.) a lower limit on the NS magnetic field is derived, which in all cases turns out to be close to the standard one and in agreement with cyclotron line measurements. The model explains the existence of super slowly rotating XPSRs without the need to hypothesize on additional accretion properties and magnetar-like magnetic fields in accreting neutron stars.
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