According to a well-known theorem of Ruh and Vilms, a conformally parameterized surface has constant mean curvature (CMC) if and only if its Gauss map is harmonic. Given a harmonic map into the 2-sphere one can construct (under suitable assumptions) a pair of conformal CMC-surfaces whose Gauss map is the given harmonic map (Bonnet, Bobenko). We will discuss a generalization of this construction and its relation to twistor theory. This is joint work with J.-H. Eschenburg.