The cyanobacterium Arthrospira platensis, spirulina, is a source of pigments such as phycobiliprotein, phycocyanin. Phycocyanin is used in the food, cosmetic, and pharmaceutical industries because of its antioxidant, anti-inflammatory, and anticancer properties. The different steps involved in extraction and purification of this protein can alter the final properties. In this review, the stability of phycocyanin (pH, temperature, and light) is discussed, considering the physicochemical parameters of kinetic modeling. The optimal working pH range for phycocyanin is between 5.5 and 6.0 and it remains stable up to 45 °C; however, exposure to relatively high temperatures or acidic pH decreases its half-life and increases the degradation kinetic constant. Phycobiliproteins are sensitive to light and preservatives such as mono- and di-saccharides, citric acid, or sodium chloride appear to be effective stabilizing agents. Encapsulation within nano- or micro-structured materials such as nanofibers, microparticles, or nanoparticles, can also preserve or enhance its stability.