Infrastructure systems are particularly vulnerable to climate hazards, such as flooding, wildfires, cyclones and temperature fluctuations. Responding to these threats in a proportionate and targeted way requires quantitative analysis of climate risks, which underpins infrastructure resilience and adaptation strategies. The aim of this paper is to review the recent developments in quantitative climate risk analysis for key infrastructure sectors, including water and wastewater, telecommunications, health and education, transport (seaports, airports, road, rail and inland waterways), and energy (generation, transmission and distribution). We identify several overarching research gaps, which include the (i) limited consideration of multi-hazard and multi-infrastructure interactions within a single modelling framework, (ii) scarcity of studies focusing on certain combinations of climate hazards and infrastructure types, (iii) difficulties in scaling-up climate risk analysis across geographies, (iv) increasing challenge of validating models, (v) untapped potential of further knowledge spillovers across sectors, (vi) need to embed equity considerations into modelling frameworks, and (vii) quantifying a wider set of impact metrics. We argue that a cross-sectoral systems approach enables knowledge sharing and a better integration of infrastructure interdependencies between multiple sectors.