The cell nucleus can be thought of as a complex, dynamic, living material, which functions to organize and protect the genome and coordinate gene expression. These functions are achieved via intricate mechanical and biochemical interactions among its myriad components, including the nuclear lamina, nuclear bodies, and the chromatin itself. While the biophysical organization of the nuclear lamina and chromatin have been thoroughly studied, the concept that liquid-liquid phase separation and related phase transitions play a role in establishing nuclear structure has emerged only recently. Phase transitions are likely to be intimately coupled to the mechanobiology of structural elements in the nucleus, but their interplay with one another is still not understood. Here, we review recent developments on the role of phase separation and mechanics in nuclear organization and discuss the functional implications in cell physiology and disease states.