This paper provides a primer on climate technology entrepreneurship, recognizing its limitations and potential adverse consequences. Climate technology entrepreneurship is needed to contribute to mitigation of and adaptation to climate change, and to help decouple economic growth from resource use. This paper identifies and describes three climate technology gaps: (i) an energy climate tech gap, an (ii) overshoot climate tech gap; and (iii) a resilience climate tech gap. The paper furthermore argues that policies for supporting climate technology entrepreneurship, including entrepreneurial ecosystems and mission-oriented approaches, have significant shortcomings. Furthermore, the paper concludes that Artificial Intelligence (AI) is unlikely to make a difference to the world’s climate change predicament. Hence, climate technology entrepreneurship is no panacea for climate change and ecological overshoot caused by human activity. On its own it will not save the world.