Functional compartmentalization is a ubiquitous hallmark of life; by segregating bio-molecules and their interactions cells achieve specialization and improved efficiency of many of their functions. In eukaryotic cells, the genetic material is known to be separated from the cytoplasm by the nuclear membrane within the few cubic micrometers of nuclear space. Recent experiment have revealed the ubiquitous presence of compartmentalization occurring at multiple scales in the nucleoplasmic environment. The driving force for these compartmentalization appears to be a juxtaposition of protein-nucleic acids phase-separation and active non-equilibrium processes. Due to the multi-scale and multi-component nature of the problem mechanistic understanding of how the interplay of thermodynamic and kinetic processes shapes the intranuclear order is lacking. During the talk, a selection of recent studies will be presented showcasing how our group uses computer simulations for probing phase-separation phenomena in cell nuclei using multi-scale physics-based models.