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In this paper we deal with the global properties of Willmore surfaces inspheres via the harmonic conformal Gauss map using loop groups.  We first derive a global description of those harmonic maps which can berealized as conformal Gauss maps of some Willmore surfaces (Theorem 3.4,Theorem 3.11 and Theorem 3.18).  Then we introduce the DPW procedure for these harmonic maps, and stateappropriate versions of the Iwasawa decomposition and the Birkhoffdecomposition Theorems. In particular, we show how the harmonic maps associatedwith Willmore surfaces can be constructed in terms of loop groups.  The third main result, which has many implications for the case of Willmoresurfaces in spheres, shows that every harmonic map into some non-compact innersymmetric space $G/K$ induces a harmonic map into the compact dual innersymmetric space $U/{(U \cap K^\mathbb{C})}$. From this correspondence we obtainadditional information about the global properties of harmonic maps intonon-compact inner symmetric spaces.  As an illustration of the theory developed in this paper we list examples(some of which were worked out in separate papers by following the theory ofthe present paper). In particular, we present an explicit, unbranched(isotropic) Willmore sphere in $S^6$ which is not S-Willmore, and thus does nothave a dual Willmore surface. This example gives a negative answer to a longopen problem (originally posed by Ejiri).

Willmore surfaces in spheres via loop groups $I$: generic cases and some examples