About six billion base pairs of DNA reside highly orderly in each human cell’s nucleus through their manifestation as twenty-three pairs of chromosomes. Delicate patterns of spatial organizations of DNA macromolecules in these eukaryotic chromosomes as well as their associated physical driving forces have, however, not been fully understood thus far. On the basis of (1) our four recent discoveries about supercoiling properties of histone H1, nucleosomes, linker DNA and polynucleosomes, (2) well-accepted six axioms about signs, shapes and handedness of DNA supercoils, and (3) our three new prepositions about correlations between DNA supercoils and chromosomal structures, we formulate new theories and models of eukaryotic chromosomal structures in the current report. It is our conclusion that all levels of chromosomal structures in eukaryotic cells are governed mainly by negative supercoils that are present in their naked linker DNA regions.