Digital twins are updated live electronic models of a system based on modelling, sensors, and processing. Structural integrity and health monitoring are facilitated by DTs. Safety of infrastructures (bridges subjected to fatigue and other damages) and vehicles (containers for dangerous goods) are subjected to dynamic loadings and accidental impacts. Therefore, continuous monitoring and structural DTs enhance their reliability and the safety of the system. Current technology is based on existing knowledge (finite element models, reduced order models, metamodels using artificial intelligence, fatigue and damage) as well as currently available technology (Internet of Things, sensors, cloud and wireless networks). A review of current work, and future developments and needs for both the construction phase and usage of assets are presented.