Digital Twins (DTs) have witnessed a paramount increase in interest in multidisciplinary engineering systems. With advancements in Structural Health Monitoring (SHM) methods and implementations, DT-based maintenance and operation stages have been implemented significantly during the life cycle of civil infrastructure. Recent literature has started laying the building blocks for incorporating the concept of DTs with SHM of large-scale civil infrastructure. This paper undertakes a systematic literature review of studies on DT-related applications for SHM of civil structures. It classifies the articles based on thematic case studies: transportation infrastructure (i.e., bridges, tunnels, roads, and pavements), buildings, off-shore marine infrastructure and wind turbines, and other civil engineering systems or assets. The proposed review is further uniquely sub-classified using diverse modelling approaches such as Building Information Modeling, Finite Element Modeling, 3D representation, surrogate and hybrid modeling used in DT implementations. This paper is solely focused on applications relating DTs to SHM practices for various civil engineering infrastructures, disregarded implementations in the fields of manufacturing, aerospace, education, health, and others, and deals with all technological advancements used in this specific field of study hence highlighting its novelty over previous reviews. Gaps and limitations emerging from the systematic review are presented, followed by the articulation of future research directions and key conclusions.