The evolution of terrestrial vertebrates, starting around 385 million years ago, is an iconic moment in evolution that brings to mind images of fish transforming into four-legged animals. Here, we show that this radical change in body shape was preceded by an equally dramatic change in sensory abilities akin to transitioning from seeing over short distances in a dense fog to seeing over long distances on a clear day. Measurements of eye sockets and simulations of their evolution show that eyes nearly tripled in size just before vertebrates began living on land. Computational simulations of these animal's visual ecology show that for viewing objects through water, the increase in eye size provided a negligible increase in performance. However, when viewing objects through air, the increase in eye size provided a large increase in performance. The jump in eye size was, therefore, unlikely to have arisen for seeing through water and instead points to an unexpected hybrid of seeing through air while still primarily inhabiting water. Our results and several anatomical innovations arising at the same time suggest lifestyle similarity to crocodiles. The consequent combination of the increase in eye size and vision through air would have conferred a 1 million-fold increase in the amount of space within which objects could be seen. The "buena vista" hypothesis that our data suggest is that seeing opportunities from afar played a role in the subsequent evolution of fully terrestrial limbs as well as the emergence of elaborated action sequences through planning circuits in the nervous system. fish-tetrapod transition | vision | visual ecology | terrestriality | prospective cognition B efore terrestrial vertebrates arose, their ancestors inhabited underwater environments, where vision is highly compromised compared with vision above water. The visual difference between life in water and life above it is comparable with driving fast on a foggy road, where our responses must be rapid and simple, vs. driving in clear daylight conditions, where deliberation over more complex choices is enabled by the vast increase in sensory range. Nonetheless, although an immense quantity of work has been done on the emergence of limbs during the evolution of land vertebrates, how visual capability changed during the transition from water to land has not been explored. In part, this lack of exploration is because computational visual ecology-necessary to interpret the fossil data-has not been combined with early tetrapod paleontology. Through combining these disciplines, here we probe the evolutionary history of the switch in our visual sensory ecology from water to air. Surprisingly, our results show that eyes tripled in size just before full-time life on land evolved. Convergent lines of evidence, including our own, strongly support the hypothesis that a crocodilian ecotype-using the greatly enhanced visual capabilities conferred by vision through air to prey on the bounty of unexploited invertebrates that long preceded the vertebrates onto ...