Curcumin, commonly used as a coloring agent as well as food additive, has exhibited great therapeutic efficacy for development of functional foods. In order to expand its applications in food, strategies are needed to tackle the poor water-solubility, bioavailability and bioaccessibility of curcumin. Nanoparticles made from individual biomaterials such as proteins, polysaccharides and lipids have been introduced and their properties have been comprehensively studied. Recently, there has been an increasing interest in nanocomplexes made from two or more biomaterials because of their ability to composite the advantages of various components. This review has specific focus on the nanocomplexes fabricated from proteins and polysaccharides. First, complexation methods with or without chemical covalent bond formation are summarized, while different methods with different degrees of complexation are discussed. The encapsulation strategies of curcumin, both traditional and newly invented, are also compared. Then, the structure and physicochemical properties of the resulting binary or ternary nanocomplexes are discussed in detail, as well as a comparison of the delivery efficiency. Last but not least, the current limitations and future directions in the development of curcumin-loaded biopolymer nanoparticles for the design of future food products are presented.