  We study the harmonic map equations for maps of a Riemann surface into a
Riemannian symmetric space of compact type from the point of view of soliton
theory. There is a well-known dressing action of a loop group on the space of
harmonic maps and we discuss the orbits of this action through particularly
simple harmonic maps called {\em vacuum solutions}. We show that all harmonic
maps of semisimple finite type (and so most harmonic $2$-tori) lie in such an
orbit. Moreover, on each such orbit, we define an infinite-dimensional
hierarchy of commuting flows and characterise the harmonic maps of finite type
as precisely those for which the orbit under these flows is finite-dimensional.
