Researchers, industry and policy-makers are considering carbon dioxide removal (CDR) methods as a way of accelerating the near-term mitigation of climate change, balancing residual emissions from hard-to-abate sectors, and addressing potential overshoot of climate targets such as the 1.5°C limit set out in the Paris Agreement. However, in many cases, CDR methods are at an early stage of research and development and raise various societal concerns – so it is crucial that it is done in a way that is responsible towards society. Responsible innovation and societal engagement involves members of the public in considerations about things that concern their interests. This helps strengthen accountability and transparency of CDR through learning from citizens, and can help to strengthen trust and legitimacy by building relationships between citizens, government and non-government actors. More broadly, it helps to build public engagement with climate change. This briefing draws on evidence from CO2RE research to examine how CDR can be better understood, communicated, appraised and governed in the UK.