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The nucleus has been viewed as a passenger during cell migration that functions merely to protect the genome. However, increasing evidence shows that the nucleus is an active organelle, constantly sensing the surrounding environment and translating extracellular mechanical inputs into intracellular signaling. The nuclear envelope has a large membrane reservoir which serves as a buffer for mechanical inputs as it unfolds without increasing its tension. In contrast, when cells cope with mechanical strain, such as migration through solid tumors or dense interstitial spaces, the nuclear envelope folds stretch, increasing nuclear envelope tension and sometimes causing rupture. Different degrees of nuclear envelope tension regulate cellular behaviors and functions, especially in cells that move and grow within dense matrices. The crosstalk between extracellular mechanical inputs and the cell nucleus is a critical component in the modulation of cell function of cells that navigate within packed microenvironments. Moreover, there is a link between regimes of nuclear envelope unfolding and different cellular behaviors, from orchestrated signaling cascades to cellular perturbations and damage.