Large-scale production of microalgae and their bioactive compounds has steadily increased in response to global demand for natural compounds. Spirulina, in particular, has been used due to its high nutritional value, especially its high protein content. Promising biological functions have been associated with Spirulina extracts, mainly related to its high value added blue pigment, phycocyanin. Phycocyanin is used in several industries such as food, cosmetics, and pharmaceuticals, which increases its market value. Due to the worldwide interest and the need to replace synthetic compounds with natural ones, efforts have been made to optimize large-scale production processes and maintain phycocyanin stability, which is a highly unstable protein. The aim of this review is to update the scientific knowledge on phycocyanin applications and to describe the reported production, extraction, and purification methods, including the main physical and chemical parameters that may affect the purity, recovery, and stability of phycocyanin. By implementing different techniques such as complete cell disruption, extraction at temperatures below 45 °C and a pH of 5.5–6.0, purification through ammonium sulfate, and filtration and chromatography, both the purity and stability of phycocyanin have been significantly improved. Moreover, the use of saccharides, crosslinkers, or natural polymers as preservatives has contributed to the increased market value of phycocyanin.