  We derive the Boltzmann equation and the collision kernel for massive
spin-1/2 particles, using the Wigner-function formalism and employing an
expansion in powers of $\hbar$. The phase space is enlarged to include a
variable related to the spin degrees of freedom. This allows to reduce the
transport equations of the independent components of the Wigner function to one
scalar equation. To next-to-leading order in $\hbar$, we find that the
collision kernel contains both local and nonlocal terms. We show that off-shell
contributions cancel in the Boltzmann equation. Our framework can be used to
study spin-polarization phenomena induced by vorticity as recently observed in
heavy-ion collisions and in condensed-matter systems.
