The spinor flow of Ammann-Weiß-Witt on a compact manifolds $M$ is a geometric flow equation for pairs $(g,\phi)$ of a Riemannian metric $g$ and a unit spinor field $\phi$ whose critical points in dimensions greater or equal to 3 are Ricci-flat Riemannian manifolds $(M,g)$ of special holonomy together with a parallel spinor field $\phi$. In my talk, I will give an introduction to this flow in the general setting and show how one may define a homogeneous version on compact homogeneous manifolds, which may also be extended to non-compact homogeneous manifolds. Moreover, I will present some results on the long-time behaviour of the usual and a volume-normalized version of the homogeneous spinor flow on specific homogeneous manifolds.