Precision Cosmology with the Lightest Elements

This is a transcript of the joint talk we gave at the Sixth Gruber Cosmology Conference at Yale University on 3 October 2025. We describe the key role played by Big Bang Nucleosynthesis (BBN) in today’s `Precision Cosmology’, focusing in particular on the precise determination of the primordial abundance of deuterium. We describe the development of the ideas and methods of BBN research from their beginnings more than 75 years ago to the latest developments, and conclude with a forward look to likely advances expected towards the end of the current decade.