The progress in polymer science and nanotechnology yields new colloidal and macromolecular objects and their combinations, which can be defined as complex polymer materials. The complexity may include a complicated composition and architecture of macromolecular chains, specific intermolecular interactions, an unusual phase behavior, and a structure of a multi-component polymer-containing material. Determination of a relation between the structure of a complex material, the structure and properties of its constituent elements, and the rheological properties of the material as a whole is the subject of structural rheology—a valuable tool for the development and study of novel materials. This work summarizes the author’s structural–rheological studies of complex polymer materials for determining the conditions and rheo-manifestations of their micro- and nanostructuring. The complicated chemical composition of macromolecular chains and its role in polymer structuring via block segregation and cooperative hydrogen bonds in melt and solutions is considered using tri- and multiblock styrene/isoprene and vinyl acetate/vinyl alcohol copolymers. Specific molecular interactions are analyzed in solutions of cellulose; its acetate butyrate; a gelatin/carrageenan combination; and different acrylonitrile, oxadiazole, and benzimidazole copolymers. A homogeneous structuring may result from a conformational transition, a mesophase formation, or a macromolecular association caused by a complex chain composition or specific inter- and supramolecular interactions, which, however, may be masked by macromolecular entanglements when determining a rheological behavior. A heterogeneous structure formation implies a microscopic phase separation upon non-solvent addition, temperature change, or intense shear up to a macroscopic decomposition. Specific polymer/particle interactions have been examined using polyethylene oxide solutions, polyisobutylene melts, and cellulose gels containing solid particles of different nature, demonstrating the competition of macromolecular entanglements, interparticle interactions, and adsorption polymer/particle bonds in governing the rheological properties. Complex chain architecture has been considered using long-chain branched polybutylene-adipate-terephthalate and polyethylene melts, cross-linked sodium hyaluronate hydrogels, asphaltene solutions, and linear/highly-branched polydimethylsiloxane blends, showing that branching raises the viscosity and elasticity and can result in limited miscibility with linear isomonomer chains. Finally, some examples of composite adhesives, membranes, and greases as structured polymeric functional materials have been presented with the demonstration of the relation between their rheological and performance properties.