This book constitutes the refereed proceedings of the 40th International Conference on Conceptual Modeling, ER 2021, which will be held as virtual event, in October 2021.The 14 full and 18 short papers were carefully reviewed and selected from 85 submissions. The conference presents topics on conceptual modeling, its foundations and applications. Celebrating its 40th anniversary this year, the overall theme of ER 2021 is: Conceptual Modeling in an Age of Uncertainty.