Concepts and methods from the physical sciences have catalyzed remarkable progress in understanding the cell nucleus in recent years. To share this excitement with physicists and encourage their interest in this field, this review offers an overview of how the physics which underlies structures and functions in the nucleus is becoming more clear thanks to methods which have been developed to simulate and study macromolecules, polymers, and colloids. The environment in the nucleus is very crowded with macromolecules, making entropic (depletion) forces major determinants of interactions. Simulation and experiments are consistent with their key role in forming membraneless compartments such as nucleoli, PML and Cajal bodies, and discrete "territories" for chromosomes. The chromosomes, giant linear polyelectrolyte polymers, exist in vivo in a state like a polymer melt. Looped conformations are predicted in crowded conditions, and have been confirmed experimentally and are central to the regulation of gene expression. Polymer theory has revealed how the chromosomes are so highly compacted in the nucleus, forming a "crumpled globule" with fractal properties which avoids knots and entanglements in DNA while allowing facile accessibility for its replication and transcription. Entropic repulsion between looped polymers can explain the confinement of each chromosome to a discrete region of the nucleus. Crowding and looping are predicted to facilitate finding the specific targets of factors which modulate activities of DNA. Simulation shows that entropic effects contribute to finding and repairing potentially lethal double-strand breaks in DNA by increasing the mobility of the broken ends, favoring their juxtaposition for repair. Signaling pathways are strongly influenced by crowding, which favors a processive mode of response (consecutive reactions without releasing substrates). This new information contributes to understanding the sometimes counter-intuitive consequences and the evolutionary advantages of a crowded environment in the nucleus.