We review here recent progress to link the nuclear organization to its function, based on elementary physical processes such as diffusion, polymer dynamics of DNA and chromatin and the search mechanism for a small target and double stranded DNA (dsDNA) break dynamics. These models and their analysis make it possible to compute critical rates involved in cell reorganization timing, which depends on many parameters. In the framework of polymer models, various empirical observations are interpreted as anomalous diffusion of chromatin at various time scales. The reviewed theoretical approaches offer a framework for extracting features, biophysical parameters, predictions, and so on, based on a large variety of experimental data, such as chromosomal capture data, single particle trajectories, and more. Combining theoretical approaches with live cell microscopy data should unveil some of the still unexplained behavior of the nucleus in carrying out some of its key function involved in survival, DNA repair, gene activation, fighting attacks and diseases.