  The group Spin(7) belongs to the list of possible holonomy of an
eight-dimensional Riemannian manifold. The weaker notion of Spin(7)-structures
plays for manifolds with holonomy Spin(7), the analogue of almost Hermitian for
K{\"a}hler manifolds. As part of a more general scheme, a notion of harmonicity
of Spin(7)-structures is developed with the objective of comparing isometric
Spin(7)-structures among themselves. We present here an account of our study in
[12] of the harmonic flow of Spin(7)-structures and its analytical properties.
