A new view of the concepts of crystallinity and crystals in synthetic macromolecules is discussed. In polymeric materials, crystallinity may be present with the concomitant occurrence of large amounts of structural disorder and in the absence of true three-dimensional long-range order. The structures of semicrystalline polymeric materials are discussed in terms of idealized limit models of crystals, where long-range order may be achieved for structural features that are not necessarily coincident with single atoms and are not necessarily point-centered. Typical examples of non-point-centered structural features are the straight lines corresponding to the chain axes of polymer molecules. This view explains the unusual ability of polymers to crystallize even in the presence of a high degree of structural disorder.