  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.
