How do banks react to firms' climate risks? Using almost 80,000 global syndicated loans originated from 2001 to 2021, we study bank lending to fossil fuel firms vis-à-vis other firms. We find that loans to fossil fuel firms are at least 7% more costly compared to other firms, and even more so toward the end of our sample. However, loan amounts to fossil fuel firms are approximately 22% larger, implying heavy financing of brown activities. We show that the pricing effects are even stronger for banks with higher reliance on ESG considerations, consistent with the shifts driven by the supply side (bank behaviour). Overall, our findings corroborate the view that banks price in climate risks but continue to heavily lend to polluting firms in the medium term (with an average maturity of four and one quarter years).