Climate change has threatened the infrastructure, operation, policymaking, and other pivotal aspects of transport systems with the accelerating pace of extreme weather events. While a considerable amount of research and best practices have been conducted for transport adaptation to climate change impacts, there is still a wide gap in the systematic assessment of climate risks on all-round transport modes (i.e., road, rail, sea, and air) with a comprehensive review and a quantitative scientific framework. This study aimed to critically review studies on how the transport sector has adapted to the impacts posed by climate change since the dawn of the 21st century. To support climate risk assessment in comprehensive transport systems, we developed a Climate Change Risk Indicator (CCRI) framework and applied it to the case of the British transport network. Focusing on a multi-modal transport system, this offers researchers and practitioners an invaluable overview of climate adaptation research with the latest tendency and empirical insights. Meanwhile, the developed CCRI framework elaborates a referable tool that enables decision-makers to employ objective data to realise quantitative risk analysis for rational transport adaptation planning.