  This is primarily a survey of the developments in the theory of harmonic maps
of finite uniton number (or unitons) which have taken place since the
introduction of extended solutions by Uhlenbeck. Such maps include all harmonic
maps from the two-sphere to a compact Lie group or symmetric space. Extended
solutions are equivalent to harmonic maps, but the advantage of extended
solutions is the fact that they are solutions to a zero curvature equation. The
closely related complex extended solutions (or complex extended frames) are in
fact even more advantageous, as has been pointed out by Dorfmeister, Pedit and
Wu. We use them to review the existing theory and also to prove some new
results concerning harmonic maps into the unitary group.
