In recent years, anthocyanins, natural dyes, have promoted great scientific and technological interest. Their intrinsic antioxidant properties and health benefits make them ideal representatives of natural dyes as replacements for synthetic dyes. However, their instability can limit their use. A promising strategy to increase the color stability of anthocyanins is their interaction with clay minerals structures. Clay minerals have characteristics favorable to the stabilization of natural dyes, such as adsorption capacity, good surface chemistry, ion exchange capacity, abundance, non-toxicity, and environmental compatibility. This review summarizes relevant works that present different clays or clay minerals as robust inorganic matrices for incorporation, improved stability, and increased resistance against the thermal- and photodegradation of anthocyanins. In addition, several authors propose different applications for the formed anthocyanin-based hybrids.