This paper provides policy-relevant insights into how climate extremes threaten transport infrastructure across Europe. Using a structured multi-hazard framework, it offers a Europe-wide assessment of the exposure of roads, railways, and inland waterways under different warming scenarios, showing that exposure to heatwaves, floods, and wildfires could increase substantially by mid-century. These findings are directly relevant to EU climate adaptation and transport policy, particularly for strategic investment in the TEN-T network. By translating complex climate data into actionable insights for infrastructure planning, the paper has strong potential to inform policymakers and engage the wider public.