Over recent decades, our understanding of climate change has accelerated greatly, but unfortunately, observable impacts have increased in tandem. Both mitigation and adaptation have not progressed at the level or scale warranted by our collective knowledge on climate change. More effective approaches to engage people on current and future anthropogenic climate change effects are urgently needed. Here, we show how species whose distributions are shifting in response to climate change, that is, ‘species-on-the-move’, present an opportunity to engage people with climate change by linking to human values, and our deep connections with the places in which we live, in a locally relevant yet globally coherent narrative. Species-on-the-move can impact ecosystem structure and function, food security, human health, livelihoods, culture and even the climate itself through feedback to the climate system, presenting a wide variety of potential pathways for people to understand that climate change affects them personally as individuals. Citizen science focussed on documenting changes in biodiversity is one approach to foster a deeper engagement on climate change. However, other possible avenues, which may offer potential to engage people currently unconnected with nature, include arts, games or collaborations with rural agriculture (e.g. new occurrences of pest species) or fisheries organisations (e.g. shifting stocks) or healthcare providers (e.g. changing distributions of disease vectors). Through the importance we place on the aspects of life impacted by the redistribution of species around us, species-on-the-move offer emotional pathways to connect with people on the complex issue of climate change in profound ways that have the potential to engender interest and action on climate change. Read the free Plain Language Summary for this article on the Journal blog.