Crystalline polymers may be affected by various kinds and amounts of structural disorder. Lack of order in polymer crystals may arise from the presence of defects in the chemical constitution, configuration and conformation and defects in the mode of packing of chains inside the crystals. Polymeric materials characterized by long range order in the parallel arrangement of chain axes and a large amount of structural disorder may be considered as solid mesophases. The different kinds and amount of disorder present in the solid mesophases of semicrystalline polymers and the possible types of solid mesophases are discussed in terms of idealized limit models of disorder. These models imply maintenance of long-range positional order, at least along one dimension, of structural features which are not necessarily point centered. Structural features, which are not point centered, are for instance chain axes, the center of mass of special groups of atoms or bundles of chains and so on. Structural aspects emerging from the X-ray diffraction analysis of several solid mesophases discussed so far in the literature are reviewed, in the light of the present analysis.