The motion of entangled polymers is marked by their ability to make conformational adjustments, which is mediated by their free ends. A credible account of the basic features of entanglement release in linear and nonlinear rheology is offered by the tube model which, despite its limitations and shortcomings, is considered as the "standard" model in the field, accounting for the dynamics of linear and branched polymers with homogeneous monomer density. Here, we challenge the two central elements of the molecular picture of entanglements by exploiting the consequences of absence of free ends and monomer density distribution. Non-concatenated ring polymers of high molar mass do not form an entanglement network with plateau modulus, but instead relax stress self-similarly, while they deform much less than their linear counterparts in nonlinear shear flow. Their rheology is extremely sensitive to the presence of unlinked linear chains. On the other hand, star polymers with many arms have a dual nature: polymeric, which governs arm relaxation, and colloidal, which controls their subsequent center-of-mass motion and completes the stress relaxation process. Appropriate choice of number and size of arms allows to tune their dynamic and structural properties, and therefore bridge the gap between polymers and colloids. These examples demonstrate a different manifestation of topological interactions, with distinct linear and nonlinear rheology, which cannot be described in full by the tube model. They also provide an avenue for taking advantage of macromolecular architecture in order to engineer the rheology of polymeric structures and soft composites. Still, a number of outstanding issues remain and we outline some perspectives in this exciting field of molecular rheology.