Following the fourth industrial revolution, and with the recent advances in information and communication technologies, the digital twinning concept is attracting the attention of both academia and industry worldwide. A microgrid digital twin (MGDT) refers to the digital representation of a microgrid (MG), which mirrors the behavior of its physical counterpart by using high-fidelity models and simulation platforms as well as real-time bi-directional data exchange with the real twin. With the massive deployment of sensor networks and IoT technologies in MGs, a huge volume of data is continuously generated, which contains valuable information to enhance the performance of MGs. MGDTs provide a powerful tool to manage the huge historical data and real-time data stream in an efficient and secure manner and support MGs' operation by assisting in their design, operation management, and maintenance. In this paper, the concept of the digital twin (DT) and its key characteristics are introduced. Moreover, a workflow for establishing MGDTs is presented. The goal is to explore different applications of DTs in MGs, namely in design, control, operator training, forecasting, fault diagnosis, expansion planning, and policy-making. Besides, an up-to-date overview of studies that applied the DT concept to power systems and specifically MGs is provided. Considering the significance of situational awareness, security, and resilient operation for MGs, their potential enhancement in light of digital twinning is thoroughly analyzed and a conceptual model for resilient operation management of MGs is presented. Finally, future trends in MGDTs are discussed.