Polysaccharides are ubiquitous in nature and represent an essential class of biopolymers with multiple levels of conformation and structural hierarchy. However, a standardized structural nomenclature, as in the case of proteins, is still lacking due to uncertainty on their hierarchical organization. In this work we use carrageenans as model polysaccharides to demonstrate that several structural levels exist and can be unambiguously resolved by statistical analysis on high resolution Atomic Force Microscopy images, supported by spectroscopic, X-ray scattering and rheological techniques. In direct analogy with proteins, we identify primary, secondary, tertiary and quaternary structures. The structure-property relationship induced by monovalent ions for kappa-, iota- and the non-gelling control lambda-carrageenan is established from the single chain regime to the occurrence of hydrogels at higher concentrations. For kappa-ccarrageenan in the presence of potassium, a disorder-order transition from random coil to single helix is first observed (secondary structure), followed by intrachain supercoiling events (tertiary structure) and macroscopic anisotropic domains which are parts of a network (quaternary structure) with tunable elasticity up to similar to 10(3) Pa. In contrast, kappa-carrageenan in the presence of sodium only produces changes in secondary structure without supercoiling events, prior to formation of gels, highlighting the ion-specificity of the process. Loosely intertwined single helices are observed for iota-carrageenan in the presence of sodium and potassium chloride, providing an elastic mesh with many junction zones, while lambda-carrageenan does not undergo any structural change. A generality of the observed behavior may be inferred by extending these observations to a distinct class of polysaccharides, the weak carboxylic polyelectrolyte Gellan gum. These results advance our understanding of ion-specific structural changes of polysaccharides and the physical mechanisms responsible for their gelation.