Andean minor tuber crops are plants domesticated and cultivated since ancient times for their edible underground parts in the Andean region. This review describes the botanical and agronomic features of Oxalis tuberosa, Tropaeolum tuberosum, and Ullucus tuberosus and reports their traditional and new uses, including the latest evidence available on their beneficial properties, complemented with observations from Peru and Bolivia. Oca has good potential to be promoted on the market for its fresh or transformed consumption, while a new promising industrial application of ulluco is the extraction of its betalains to be used as natural food colorants. Finally, mashua, for its high contents of antioxidants and anticarcinogenic properties, is highly relevant to the nutraceutical sector. The use of the three crops in gourmet restaurants of the Andean region has increased notably during the last decade, which suggests that their demand might increase in the future as they become more popular.