We review the work done on complexes between biopolyelectrolytes such as ionically modified cellulose or chitosan and oppositely charged surfactants. Around equimolarity of the charges one typically observes precipitation but for other mixing ratios one may form long-time stable complexes, where structure and rheology depend on the mixing ratio, total concentration and the molecular constitution of the components. In addition, it may be the case that the structures are formed under non-equilibrium situations and therefore depend on the preparation path. The binding is shown to occur cooperatively and the micelles present often retain their shape irrespective of the complexation. However, the rather stiff biopolyelectrolytes may lead to an interconnection between different aggregates thereby forming a network with the corresponding rheological properties. In general, the structure and the properties of the aggregates are rather versatile and correspondingly one can create a wide range of different surfactant-biopolyelectrolyte systems by appropriately choosing the composition. This is very interesting as it allows for formulations with a large range of tuneable properties with ecologically friendly polyelectrolytes for many relevant applications.