Cohesion matters! The correlation between the conformational rigidity of the polyelectrolyte and the size and stability of the globular assembly is discussed in this review article. Some examples of models for the association of polyelectrolytes to globular assemblies are shown here.Supramolecular complexes of strong polyelectrolytes and oppositely charged ionic micelles or protein assemblies derive their main stabilization from electrostatic interactions that include the counterion condensation/release mechanism and from hydrophobic interactions distributed along apolar sections of the components. The predicted and the experimental behavior of selected complexes differing in the flexibility of the polyelectrolyte and in the cohesion of the complementary assembly is reviewed and analyzed. Depending upon the rigidity of the polyelectrolyte, globular surfactant clusters persist in the final structure or are transformed into elongated assemblies. On the other hand, even the rather rigid DNA molecule is forced to bend by strongly associated cationic protein complexes such as the histone octamers. A general framework should allow the prediction of these structures in terms of the interplay between the persistence length of the polyelectrolyte and the association constant of the protein or the surfactant assembly.