In recent years, Digital Twins (DT) have been implemented in different industrial sectors, in several applications areas such as design, production, manufacturing, and maintenance. In particular, maintenance is one of the most researched applications, as the impact of the execution of maintenance task may have a great impact in the business of the companies. For example, in sector such as energy or manufacturing, a maintenance activity can cause the shutdown of an entire production line, or in the case of a wind turbine inspection, may face the safety of an operator to measure a simple indicator. Hence, the application of more intelligent maintenance strategies can offer huge benefits. In this context, this paper focuses on the review of DT applications for maintenance, as no previous work has been found with this aim. For instance, both "Digital Twin" and "maintenance" concepts and strategies are described in detail, and then a literature review is carried out where these two concepts are involved. In addition to identifying and analyzing how DTs are currently being applied for maintenance, this paper also highlights future research lines and open issues.