Linear infrastructures, such as railways, tunnels, and pipelines, play essential roles in economic and social development worldwide. However, under the influence of geohazards, earthquakes, and human activities, linear infrastructures face the potential risk of damage and may not function properly. Current monitoring systems for linear infrastructures are mainly based on non-contact detection (InSAR, UAV, GNSS, etc.) and geotechnical instrumentation (extensometers, inclinometers, tiltmeters, piezometers, etc.) techniques. Regarding monitoring sensitivity, frequency, and coverage, most of these methods have some shortcomings, which make it difficult to perform the accurate, real-time, and comprehensive monitoring of linear infrastructures. Distributed acoustic sensing (DAS) is an emerging sensing technology that has rapidly developed in recent years. Due to its unique advantages in long-distance, high-density, and real-time monitoring, DAS arrays have shown broad application prospects in many fields, such as oil and gas exploration, seismic observation, and subsurface imaging. In the field of linear infrastructure monitoring, DAS has gradually attracted the attention of researchers and practitioners. In this paper, recent research and the development activities of applying DAS to monitor different types of linear infrastructures are critically reviewed. The sensing principles are briefly introduced, as well as the main features. This is followed by a summary of recent case studies and some critical problems associated with the implementation of DAS monitoring systems in the field. Finally, the challenges and future trends of this research area are presented.