In the Industry 4.0 era, the Digital Twin has become one of the most promising enabling technologies supporting material flow. Although the literature on the Digital Twin is becoming relatively well explored, including a certain number of review papers, the context of the Digital Twins application in internal transport systems has not been investigated so far. This paper thoroughly reviews the research on the Digital Twins applied in internal transport systems concerning major research trends within this research area and identification of future research directions. It provides clarification of various definitions related to the Digital Twin concept, including misconceptions such as a digital shadow, a digital model, and a digital mirror. Additionally, the relationships between terms such as material handling, material flow, and intralogistics in the context of internal transport systems coupled with the Digital Twin are explained. This paper’s contribution to the current state of the art of the Digital Twins is three-fold: (1) recognition of the most influential and high-impact journals, papers, and researchers; (2) identification of the major research trends related to the Digital Twins applications in internal transport systems, and (3) presentation of future research agendas in investigating Digital Twins applied for internal transport systems.