Anthocyanins are water-soluble pigments found in plants. They exist in various colors, including red, purple, and blue, and are utilized as natural colorants in the food and cosmetics industries. The pharmaceutical industry uses anthocyanins as therapeutic compounds because they have several medicinal qualities, including anti-obesity, anti-cancer, antidiabetic, neuroprotective, and cardioprotective effects. Anthocyanins are conventionally procured from colored fruits and vegetables and are utilized in the food, pharmaceutical, and cosmetic industries. However, the composition and concentration of anthocyanins from natural sources vary quantitively and qualitatively; therefore, plant cell and organ cultures have been explored for many decades to understand the production of these valuable compounds. A great deal of research has been carried out on plant cell cultures using varied methods, such as the selection of suitable cell lines, medium optimization, optimization culture conditions, precursor feeding, and elicitation for the production of anthocyanin pigments. In addition, metabolic engineering technologies have been applied for the hyperaccumulation of these compounds in varied plants, including tobacco and arabidopsis. In this review, we describe various strategies applied in plant cell and organ cultures for the production of anthocyanins.