The potato (Solanum tuberosum L.) is a tuber that is largely used for food and is a source of different bioactive compounds such as starch, dietary fiber, amino acids, minerals, vitamins, and phenolic compounds. Phenolic compounds are synthetized by the potato plant as a protection response from bacteria, fungi, viruses, and insects. Several works showed that these potato compounds exhibited health-promoting effects in humans. However, the use of the potato in the food industry submits this vegetable to different processes that can alter the phenolic content. Moreover, many of these compounds with high bioactivity are located in the potato’s skin, and so are eliminated as waste. In this review the most recent articles dealing with phenolic compounds in the potato and potato byproducts, along with the effects of harvesting, post-harvest, and technological processes, have been reviewed. Briefly, the phenolic composition, main extraction, and determination methods have been described. In addition, the “alternative” food uses and healthy properties of potato phenolic compounds have been addressed.