Climate leaders can elevate the performance of others to act more ambitiously, thus fulfilling a vital role in an urgent context. What we may consider to be ‘climate leadership’ has been refined conceptually over time, and here we outline the main tenets identified in the literature, emphasising four leadership ‘types’ and two ‘styles’. While doing so, we also problematise the existing assumption that ‘climate leadership’ refers only to leadership towards more ambitious action, and introduce ‘negative climate leadership’. We then examine European Union climate leadership across three dimensions: i) leadership within the EU, as part of a ‘polycentric’ governance model; ii) the EU’s fluctuating credentials as a leader within global climate negotiations; and iii) the EU’s broader external climate governance. We summarise and reflect upon a growing literature, analyse EU climate leadership alongside the factors that shape it and its impacts, and propose new areas for research.