Cosmology is famously an observational rather than an experimental science. No experimentalists were present in the early universe, and the birth and subsequent evolution of the universe cannot be repeated. Instead, we can only measure the spatial correlations between cosmological structures at late times. A central challenge of modern cosmology is to construct a consistent history of the universe that explains these correlations. In this colloquium, I will describe a new approach to determine cosmological correlations from consistency conditions alone, following a perspective familiar from the study of scattering amplitudes. I will present an intriguing connection between scattering amplitudes and cosmological correlators, and discuss how recent breakthroughs in the field of scattering amplitudes could lead to new insights into the structure of cosmological correlations.