DNA molecules are long polymers that are packaged inside biological cells. These are much longer than the typical cell diameter, especially in humans. For example, if the human DNA had the dimensions of a fishing line, and the human cell was the size of an airplane hand luggage, the DNA would reach from Ystad to Tromsö (~2000 km). But it is not only carefully packaged. DNA also folds to allow access to the genetic code by various biomolecules, such as transcription factors and RNA polymerases. In other words, the DNA must be dense enough to fit in the nucleus and manageable. However, the molecular mechanisms behind how the cell achieves this is an open problem. We use several approaches to understand the structure-function relationship of DNA folding. First, we use methods from complex network theory that we apply to empirical data sets (so-called Hi-C data) to find biologically significant 3D communities. Second, we simulate stochastic lattice models to understand how specific genetic elements called insulators block pairwise DNA-DNA contacts that aim to activate genes. These simulations are based on the Gillespie algorithm (sometimes also called Dynamic Monte Carlo). Third, we use polymer simulations to help get a better mechanistic understanding of how select groups of DNA-binding proteins locally fold DNA into dense crumples. These crumples may determine if genes turn on or off.