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Modern society strongly relies on critical infrastructures such as telecommunications, transport networks, and the supply of gas, water, and energy. Such infrastructures, which are often exposed to natural hazards, can cause significant damage when disrupted. Among the different strategies to prevent these disruptions and cope with preparedness, mathematical models can be used to support managers in several approaches, as classification and estimation problems using machine learning, vulnerability quantification on complex networks, and survivability analysis. Nevertheless, the assessment of these quantities demands a solid conceptual discussion. In this chapter, we explore concepts of non-linear dynamics, complex systems, machine learning, and survivability analysis in the context of disaster risk reduction.