For the last one century, the crystal structure of atactic poly(vinyl alcohol) (at-PVA) is assumed to have been established on the basis of the quantitative analysis of X-ray diffraction data. A similar situation is also seen for the crystal structure of PVA-iodine complex. However, it has been found that these crystal structures cannot reproduce the recently measured wide-angle neutron diffraction data satisfactorily. This dilemma between the X-ray and neutron diffraction data analyses was solved totally by the introduction of structure disorder into the previously proposed regular structure models. The concept of disorderliness has allowed us to interpret the characteristic structural features of these substances more concretely: (i) PVA crystals show a preferential orientation of the 110 planes along the rolled plane of the doubly oriented sample. The 110 planes are composed of hydrogen-bonded sheets of zigzag chains, which cause the disorderliness because of the easy slippages by the application of shear stress. (ii) In the formation mechanism of the PVA-iodine complex, the disordered packing structure of PVA and iodine ions is formed at first (form I), and it develops to form II with more or less regularly packed PVA-iodine layers, reaching finally the structure of form III with regularly arrayed PVA-iodine layers. The present study is one good example to show the significance of the coordinated analysis of X-ray and neutron diffraction data for erasing the ambiguities of the previously proposed crystal structure of a synthetic polymer.