  First, I study the analogy between the magnetization of a material and the
spin polarization of particles in a fluid. Using the relativistic version of
the Barnett effect, i.e. the magnetization of a material induced by mechanical
rotation, the spin polarization induced by thermal vorticity is obtained within
a purely classical model, where spin is treated as an intrinsic magnetic moment
and rotation is included as a non-inertial effect. I argue that since spin
polarization induced by thermal vorticity can be obtained in a classical
theory, it can not be dominated by quantum anomalies.
  Second, the spin polarization induced by magnetic field is obtained for a
fluid at local thermal equilibrium using statistical quantum field theory. The
obtained formula is valid beyond the weak field approximation and when
contributions from the non-homogeneity of the magnetic field are small. The
exact form of spin polarization is studied for a free Dirac field at global
equilibrium, and, like magnetic susceptibility, it oscillates according to the
de Haas - van Alphen effect.
  Finally, I briefly review how magnetic field contributes to the difference
between the spin polarization of $\Lambda$ and $\bar{\Lambda}$ observed in
heavy-ion collisions.
