Over the past two decades, the biomechanical properties of cells have emerged as key players in a broad range of cellular functions, including migration, proliferation, and differentiation. Although much of the attention has focused on the cytoskeletal networks and the cell's microenvironment, relatively little is known about the contribution of the cell nucleus. Here, we present an overview of the structural elements that determine the physical properties of the nucleus and discuss how changes in the expression of nuclear components or mutations in nuclear proteins can not only affect nuclear mechanics but also modulate cytoskeletal organization and diverse cellular functions. These findings illustrate that the nucleus is tightly integrated into the surrounding cellular structure. Consequently, changes in nuclear structure and composition are highly relevant to normal development and physiology and can contribute to many human diseases, such as muscular dystrophy, dilated cardiomyopathy, (premature) aging, and cancer.