The 20th century saw the establishment of the first quantitative theory seeking to describe the behaviour of the Universe as a whole – the Big Bang. This sets up a framework within which there has been great success in interpreting a wide range of observations, including the abundances of light chemical elements, the existence and spectrum of the cosmic microwave radiation, and the formation and evolution of galaxies. At the end of the 20th century, the surprising conclusion of the Big Bang theory is that 95% of the Universe is made of two different unknown types of material whose nature remains unclear: dark matter and dark energy. Needless to say, this is a major challenge for science. At the beginning of the 21st century, cosmology appears poised to enter a high-precision era, where the key quantities of cosmology will be determined to two or more significant figures. If cosmologists are on the right track, this will confirm the existence of dark matter and dark energy; if not, it will force us to revise our current picture of the Universe. Either way, the prospect is for exciting years ahead in cosmology.