Observations made using large ground-based and space-borne telescopes have probed cosmic history from the present day to a time when the Universe was less than one-tenth of its present age. Earlier still lies the remaining frontier, where the first stars, galaxies and massive black holes formed. They fundamentally transformed the early Universe by endowing it with the first sources of light and chemical elements beyond the primordial hydrogen and helium produced in the Big Bang. The interplay of theory and upcoming observations promises to answer the key open questions in this emerging field.