High-impedance faults (HIFs) represent one of the biggest challenges in power distribution networks. An HIF occurs when an electrical conductor unintentionally comes into contact with a highly resistive medium, resulting in a fault current lower than 75 amperes in medium-voltage circuits. Under such condition, the fault current is relatively close in value to the normal drawn ampere from the load, resulting in a condition of blindness towards HIFs by conventional overcurrent relays. This paper intends to review the literature related to the HIF phenomenon including models and characteristics. In this work, detection, classification, and location methodologies are reviewed. In addition, diagnosis techniques are categorized, evaluated, and compared with one another. Finally, disadvantages of current approaches and a look ahead to the future of fault diagnosis are discussed.