In education and creative industries, ordinary workplaces and everyday life, curiosity is widely regarded as a good thing, worthy of encouragement and support. This raises practical questions about how to be more curious and encourage curiosity in others. To bring these questions into focus, it helps to think geographically, asking: how can we find and make ‘space’ for curiosity? But curiosity is not simply a practical problem. Through spaces for curiosity, it is possible to raise more fundamental questions about what curiosity is and what it can be: about who can be curious, and what curiosity is for.