Climate change is one of the most critical challenges of our time, requiring significant responses from all aspects of society, including education. The prevailing responses to climate change tend towards treating the crisis as a predominantly scientific and managerial issue that requires technological solutions or behaviour changes. Correspondingly, climate change education (CCE) often focuses on teaching climate science and (predominantly individual) behaviour change. We argue that CCE, as part of a broader environmental and sustainability education (ESE), needs, in addition to a short-term damage limitation response, a simultaneous, longer-term, transformational approach that goes beyond critical humanism and engages with posthumanism. We explore ideas about human continuity with the more-than-human world, and the relationality and materiality of humans. Drawing on recent developments within posthuman pedagogies research, we consider how posthumanism might influence ESE/CCE, focussing on how two sustainability competency frameworks, UNESCO's key competencies and the EU's GreenComp, might be posthumanised.