There is a vast class of properties that science has so far almost entirely neglected. These properties are central to an understanding of physical reality both at an everyday level and at the level of fundamental phenomena, yet they have traditionally been thought of as impossible to incorporate into fundamental explanations. They relate not only to what is true – the actual – but to what could be true – the counterfactual. This is the science of can and can’t. Chiara Marletto, a pioneer in this field, explores the promise that this fascinating, far-reaching approach holds not only for revolutionizing how fundamental physics is formulated, but also for confronting existing technological challenges, from delivering the next generation of information-processing devices to designing AI. In each chapter, Marletto sets out how counterfactuals can solve a vexed open problem in science, and demonstrates that by contemplating the possible as well as the actual, we can break down barriers to knowledge and form a more complete and fruitful picture of the universe.