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The European Center for Atomic and Molecular Calculation (CECAM) promotes fundamental research on advanced computational methods and their application to important problems in science and technology. Over its 50 years of service, CECAM has extended its focus from atomistic and molecular simulations to a wide range of problems in materials science, biology, and medicinal chemistry. CECAM fosters the development of computer simulation as a new way of linking theory and experiment, with a growing interest in multiscale modeling and data-driven initiatives like machine learning and artificial intelligence. With 18 nodes established across Europe, Israel, and the US, CECAM organizes scientific workshops, advanced schools, collaborative research projects, and an international visitors program to advance computational science and inspire productive collaborations.