The potential for widespread and catastrophic impacts of extreme events, especially those related to climate change effects, has never been greater in society than today. Rapid urbanization does not only mean higher concentrations of population and economic activities in urban areas, but also increasing complexity and infrastructure interdependencies in the delivery of critical urban services such as energy, water, transport and communication. This paper reviews the current literature in these areas and identifies critical research and development (R&D) challenges from the perspective - and for the benefit - of key stakeholders, considering the primary decision goals and context. From this vantage point, the critical evaluation framework is extended to include a classification of disruptions and extreme events, and an overview of infrastructure modeling and simulation approaches, and broader socio-economic impact assessment methods. Mapping the modeling and assessment methods against different decision-making contexts, critical gaps in knowledge and tools are identified to support the latter. A decision support framework is presented to select an appropriate method when analyzing the impacts of a disruption to infrastructure systems. Emerging R&D and science gaps and challenges including how to deal with "black swans" and "perfect storms" in relation to infrastructure disruptions caused by extreme events are identified. These are characterized by deep uncertainties in every major component in the information chain - from the frequency and intensity of a disruptive event, to assessing the first order and immediate impacts of an infrastructure failure, to estimating the nature, extent and impact of cascading failures.