A structural digital twin links a physical structure in the real world with a digital counterpart in the virtual world using the data from the real system to improve predictive performance and decision-making for operators and asset managers. Finite element models (FEMs) are commonly used as advanced structural simulation in digital twining. FEM inaccuracies due to errors and uncertainties, as well as their computational-heavy nature, however, call for automated (or semi-automated) model updating methods. Such methods calibrate the discrepancy between numerical finite element models and the actual behavior of the structure. In broad terms, model updating can be divided into two classes: data-driven and physic-driven methods. While both methods have their merits and shortcomings, a new area of study, referred to as physics-informed machine learning (PIML), tries to leverage the advantage of machine learning methods and combine the underlying physic. From these methods, physics-informed neural networks (PINNs) have started to gain popularity in structural applications. This paper aims to provide a review of the most recent applications of PINNs in the body of knowledge for civil structures. The paper first introduces model updating by highlighting different methods proposed in the literature. Secondly, PIML will be presented with a focus on PINN and its extended methods. Finally, PINN applications in the digital twinning of civil infrastructure systems will be discussed, and the need for future developments will be highlighted. This study can give insight into the application and capabilities of PINNs in structural engineering and digital twinning.