DNA folding induced by polyion complexion with cationic polyelectrolytes (or catiomers) is attracting remarkable attention in the context of nucleosome formation during genome packaging and gene vector preparation. The application of block catiomers, in contrast to homocatiomers, is attractive because the spontaneously formed polyplex micellar structure can suppress the occurrence of secondary aggregation, allowing the folding of a single DNA molecule. Here, DNA is folded to form several higher-order structures, including rod-shaped, globular, and ring-shaped (toroid) structures. This review discusses the origin of this versatile higher-order structure formation by addressing the conditions and potential mechanisms underlying when and how DNA is organized into these structures upon complexation with block catiomers. DNA undergoes large volume transition to organize several higher-order structures, including globular, rod-shaped, and ring-shaped (toroid) structures by polyion complexation with block copolymer comprising hydrophilic segment and polycations. This review discusses the origin of this versatile higher-order structure formation. The knowledge of underlying physical mechanisms might ultimately improve our understanding of the formation of hierarchically ordered structures in the nucleosomes and the operating principles governing how DNA functionality emerges, and also provide a solid strategy to prepare structured nonviral gene vectors.