There is multitude of models available to assess structural safety based on a set of input parameters. As the degree of complexity of the models increases, the uncertainty of their output tends to decrease. However, more complex models typically require more input parameters, which may contain a higher degree of uncertainty. Therefore, it becomes necessary to find the balance that, for a particular scenario, will reduce the overall uncertainty (model + parameters) in structural safety. The latter is the objective of the Marie Skłodowska-Curie Innovative Training Network titled TRUSS (Training in Reducing Uncertainty in Structural Safety) funded by the EU Horizon 2020 research and innovation programme (http://trussitn.eu). This paper describes how TRUSS addresses uncertainty in: (a) structural reliability of materials such as basalt fiber reinforced polymer, (b) testing techniques in the assessment of concrete strength in buildings, (c) numerical methods in computing the non-linear response of submerged nuclear components subjected to an earthquake, (d) estimation of life of wind turbines, (e) the optimal inspection times and management strategies for ships, (f) characterization of the dynamic response of ship unloaders and (g) the relationship between vehicles fuel consumption and pavement condition.