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The human genome is folded in complex, non-random three-dimensional conformations within the cell nucleus, as highlighted by novel biochemical and microscopy technologies. Importantly, such complex architecture is involved in vital cell functions, controlling gene expression, whereas abnormal chromosome folding can result in diseases. In this talk, I discuss how massive data on genome architecture, generated thanks to recent experimental advances, can be explained in a principled approach based on the statistical mechanics of polymers. I also discuss how such models can be powerful tools to make sensible predictions in silico, such as how genetic mutations result in diseases, opening the way to novel medical applications.