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[Display omitted] • Natural pigments can be complexed with biopolymers (BP) by using several techniques. • Complexation can improve the stability and bioaccessibility of natural pigments (NP). • Proteins and polysaccharides are the most common BP used as wall materials to NP. • Different techniques can be used to obtain the binding properties involved in NP-BP complex formation. • Thermodynamic parameters of complex formation can provide information about the stability of NP-BP complexes. Natural pigments are bioactive compounds that can present health-promoting bioactivities in the human body. Due to their strong coloring properties, these compounds have been widely used as color additives as an alternative to artificial colorants. However, since these pigments are unstable under certain conditions, such as the presence of light, oxygen, and heat, the use of complexation and encapsulation techniques with biopolymers is in demand. Moreover, some functional properties can be achieved by using natural pigments-biopolymers complexes in food matrices. The complexation and encapsulation of natural pigments with biopolymers consist of forming a complex with the aim to make these compounds less susceptible to oxidative and degrading agents, and can also be used to improve their solubility in different media. This review aims to discuss different techniques that have been used over the last years to create natural pigment-biopolymers complexes, as well as the recent advances, limitations, effects, and possible applications of these complexes in foods. Moreover, the understanding of thermodynamic parameters between natural pigments and biopolymers is very important regarding the complex formation and their use in food systems. In this sense, thermodynamic techniques that can be used to determine binding parameters between natural pigments and potential wall materials, as well as their applications, advantages, and limitations are presented in this work. Several studies have shown an improvement in many aspects regarding the use of these complexes, including increased thermal and storage stability. Nonetheless, data regarding the biological effects on the human body and the sensory acceptance of natural pigments-biopolymers complexes in food systems are scarce in the literature. [ABSTRACT FROM AUTHOR]