Infrastructure systems are important for social development and economic growth. They play a fundamental role in the use and distribution of spatial services, such as transportation and communication. Recent historical events such as the 2002 European flood, hurricane Katrina (2005), or the Tōhoku earthquake and tsunami (2011) have shown that the analysis and understanding of large-scale infrastructure systems are essential for research, engineering and society. Especially due to the complexity and interdependence of these systems, localised failures can cascade dramatically, leading to widespread, unforeseen and often disproportionate disruptions compared to the actual physical damage. Infrastructure managers plan and execute interventions to guarantee the operational state of their infrastructures under various circumstances. This also applies in the aftermath of natural hazard events. As the resources available to managers to protect their infrastructures are limited, it is essential for them to be aware of the probable consequences (i.e., risk) in order to set priorities and be resource-efficient. In order to support infrastructure managers in their risk assessments, this work aims to develop a methodology and corresponding techniques to understand and quantify the risk of complex infrastructure systems affected by natural hazards, considering spatial and temporal aspects. The first part of this work focuses on the development of a risk assessment process for infrastructure systems affected by natural hazards using computational models to simulate different hazard scenarios and estimate the associated consequences. In this part, a general risk assessment process for infrastructure systems affected by natural hazards is introduced. Based on this process a simulation engine is presented which is constructed as a computational platform to estimate risk by supporting the combination of models from different disciplines. This allows the application of the proposed process to estimate the spatio-temporal risk of a realistic road network due to the occurrence of time-varying multi-hazard events, considering physical and functional effects on network objects (e.g. bridges and road sections), the functional interrelationships of the affected objects, the resulting probable consequences, duration of network disruption, and the restoration of the network. To give better insights into the resilience of the infrastructure system to natural hazards and to help the infrastructure managers to make better decisions in such situations, a restoration model is formulated to determine optimal recovery responses in the aftermath of such events. While the implementation of the risk assessment process in the first part is mainly based on computational models, the second part focuses on the development of innovative mathematical models from the field of network sciences. First, a network model for interdependent infrastructure systems is presented, which is based on the mathematical concept of the spatially embedded random network, and therefore, needs only a limited amount of data. Second, a complex network approach is used to investigate traffic flow dynamics on road networks, which provides reasonable estimates for traffic flow changes and significantly reduces the computing time of classical simulation models. These models can be used to support the risk assessment of complex infrastructure systems in terms of data requirements and computing power, i.e. computational models can be substituted if only limited data is available, or a decrease in the computational effort is required. This work contributes to the field of risk assessment and its application to complex infrastructure systems, by providing a methodology and corresponding techniques to understand and quantify the risk of complex infrastructure systems, affected by natural hazards, considering spatial and temporal aspects. More precisely, this work provides a novel risk assessment process for infrastructure managers, designed to estimate the spatio-temporal risk of complex infrastructure systems due to the occurrence of time-varying multi-hazard events. In doing so, it not only extends the state-of-the-art research in this field but also helps to provide decision support for infrastructure managers.