The IAU Centenary Symposium was held at its General Assembly in Vienna in 2018. It starts with plenary lectures, by Malcolm Longair on 100 years of astronomy, astrophysics and cosmology, and by Catherine Cesarsky, who reflects on a century of IAU history. There follows reminiscences from past IAU presidents and general secretaries and presentations on various aspects of IAU history, including some of the famous astronomers who served the Union. The volume then examines the relations between the IAU and different geographical regions, including the issues relating to the Central Powers after World War I, and the 'China crisis', when China withdrew from the Union in 1960 and was absent for two decades. The IAU's internal structures and organization are reviewed, along with trends in astronomical publishing and astronomical education. IAU S349 finishes with a vision of the IAU's future from its current president, Ewine van Dishoeck.