In the face of climate change, reinforced concrete (RC) bridges encounter significant risks, indicating the need for effective adaptation measures. This paper explores the co-benefits of climate change adaptation for RC bridges and how sustainability and resilience can be achieved through adaptation measures. It also investigates the integration of climate change adaptation into Eurocode standards. The chosen approach includes mapping and analysing (i) climate change impacts on RC bridges and (ii) the co-benefits of different adaptation measures. Moreover, it includes an examination of the current generation of Eurocodes and an exploration of barriers and proposed actions towards climate change adaptation. The research highlights the complex relationships and compound effects characterising climate change impacts on RC bridges and the co-benefits of several adaptation measures. Moreover, it emphasises gaps in existing Eurocodes that need to be addressed to achieve climate change adaptation. Future actions, such as the economic viability of adaptation measures, their long-term performance, and the trade-offs of the bridge’s life extension, especially for measures non-sustainable at first glance, should be further investigated.