The nuclear lamina, a conserved structure in metazoans, provides mechanical rigidity to the nuclear envelope. A decrease in lamin levels and/or lamin mutations are associated with a host of human diseases. Despite being only about 15 nm thick, perturbation of components of the nuclear lamina dramatically impacts the deformation response of the entire nucleus through mechanisms that are not well understood. Here we discuss evidence for the recently proposed 'nuclear drop' model that explains the role of A-type lamins in nuclear deformation in migrating cells. In this model, the nuclear lamina acts as an inextensible surface, supporting a surface tension when fully unfolded, that balances nuclear interior pressure. Much like a liquid drop surface where the molecularly thin interface governs surface tension and drop shape under external forces, the thin nuclear lamina imparts a surface tension on the nuclear drop to resist nuclear deformation as well as to establish nuclear shape. We discuss implications of the nuclear drop model for the function of this crucially important eukaryotic organelle.