Gene regulation programs establish cellular identity and rely on dynamic changes in the structural packaging of genomic DNA. The DNA is packaged in chromatin, which is formed from arrays of nucleosomes displaying different degree of compaction and different lengths of inter-nucleosomal linker DNA. The nucleosome represents the repetitive unit of chromatin and is formed by wrapping 145-147 basepairs of DNA around an octamer of histone proteins. Each of the four histones is present twice and has a structured core and intrinsically disordered terminal tails. Chromatin dynamics are triggered by inter- and intra-nucleosome motions that are controlled by the DNA sequence, the interactions between the histone core and the DNA, and the conformations, positions, and DNA interactions of the histone tails. Understanding chromatin dynamics requires studying all these features at the highest possible resolution. For this, molecular dynamics simulations can be used as a powerful complement or alternative to experimental approaches, from which it is often very challenging to characterize the structural features and atomic interactions controlling nucleosome motions. Molecular dynamics simulations can be performed at different resolutions, by coarse graining the molecular system with varying levels of details. Here we review the successes and the remaining challenges of the application of atomic resolution simulations to study the structure and dynamics of nucleosomes and their complexes with interacting partners.