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In 1948, Hendrik Casimir predicted that a generalized version of van der Waals forces would arise between two metal plates due to quantum fluctuations of the electromagnetic field. These forces become significant in micromechanical systems at submicrometre scales, such as in the adhesion between movable parts. The Casimir force, through a close connection to classical photonics, can depend strongly on the shapes and compositions of the objects, stimulating a decades-long search for geometries in which the force behaves very differently from the monotonic attractive force first predicted by Casimir. Recent theoretical and experimental developments have led to a new understanding of the force in complex microstructured geometries, including through recent theoretical predictions of Casimir repulsion between vacuum-separated metals, the stable suspension of objects and unusual non-additive and …