  In the past decades, the authors made some systematic research on global and
local properties of Willmore surfaces in terms of the DPW method. In this note
we give a survey, mainly including the basic framework of the DPW method for
the global geometry of Willmore surfaces via the conformal Gauss map,
applications on constructions of Willmore $2$-spheres, characterizations of
minimal surfaces, Willmore deformations of Willmore surfaces and Bjoerling
problems for Willmore surfaces. Moreover, we also obtained some results on
harmonic maps via DPW, including a duality theorem for harmonic maps into an
inner non-compact symmetric space and its dual inner compact symmetric space,
and harmonic maps of finite uniton type.
