Changes in the shape and structural organization of the cell nucleus occur during many fundamental processes including development, differentiation and aging. In many of these processes, the cell responds to physical forces by altering gene expression within the nucleus. How the nucleus itself senses and responds to such mechanical cues is not well understood. In addition to these external forces, epigenetic modifications of chromatin structure inside the nucleus could also alter its physical properties. To achieve a better understanding, we need to elucidate the relationship between nuclear structure and material properties. Recently, new approaches have been developed to systematically investigate nuclear mechanical properties. These experiments provide important new insights into the disease mechanism of a growing class of tissue-specific disorders termed 'nuclear envelopathies'. Here we review our current understanding of what determines the shape and mechanical properties of the cell nucleus.