In 1905, the biologist Edmund Selous marveled at the sight of a flock of starlings in flight, describing it as “they circle; now dense like a polished roof, now disseminated like the meshes of some vast all-heaven-sweeping net…wheeling, rending, darting…a madness in the sky.” He speculated, “They must think collectively, all at the same time, or at least in streaks or patches — a square yard or so of an idea, a flash out of so many brains.” Over a century later, we still have much to learn about how social interactions connect individual brains, enabling sensing and information processing in mobile animal groups, such as schooling fish. Using a combination of modeling, automated tracking, computational reconstruction of sensory information, immersive ‘holographic’ virtual reality (VR) experiments, and experiments with bio-mimetic robotic fish, I will discuss how and why fish school. I will reveal that there exist geometric principles underlying collective sensing and decision-making. These principles span multiple scales of biological organization—from neural dynamics to individual decision-making, and from individuals to collectives. In doing so, I will present a minimal mechanistic model that accounts for how schooling emerges in nature, revealing how brain and behavioural synchronization give rise to collective intelligence. Additionally, I will demonstrate how we are increasingly able to study massive fish schools in the wild, as well as how our findings can inspire human-engineered systems, including robust bio-mimetic control laws for collective robotics.