This chapter gives an introduction to risk-based vulnerability assessment of urban infrastructure regarding the consequences of climate change, by describing an approach developed as part of the EU-funded research and innovation project Climate Resilient Cities and Infrastructures. The approach is modular, widely applicable, and supported by a suite of software tools. It guides practitioners and end-users through the process of risk-based vulnerability assessment of urban systems, including built-up areas and (critical) infrastructure. How the approach can be adapted to and applied in a local context is demonstrated via its exemplary application in case studies with the four European cities Bilbao (Spain), Bratislava (Slovakia), Greater Manchester (United Kingdom), and Paris (France). Essential concepts for risk and vulnerability assessments and the current state of the art from related research projects are discussed before a detailed description of the developed approach and its supporting tools is given.