The 2016 Hintze Biannual Lecture delivered by Professor Robert Kennicutt Understanding the birth of stars is one of grand challenges of 21st century astrophysics, with impacts extending from the formation of planets to the birth and shaping of galaxies themselves. The challenge has been all the more difficult because the most active birth sites are largely hidden in visible light. Thanks to a new generation of infrared and submillimetre space telescopes this veil has been lifted, and a complete picture of starbirth in the Universe is emerging. They reveal an extraordinary diversity of activities in galaxies, and an emerging history of star formation cosmic time, extending back to some of the first stars and seeds of galaxies. This talk will summarise what we have learnt about starbirth on cosmic scales, and highlight the challenges and opportunities which lie ahead.