While the genetic information is contained in double helical DNA, gene expression is a complex multilevel process that involves various functional units, from nucleosomes to fully formed chromatin fibers accompanied by a host of various chromatin binding enzymes. The chromatin fiber is a polymer composed of histone protein complexes upon which DNA wraps, like yarn upon many spools. The nature of chromatin structure has been an open question since the beginning of modern molecular biology. Many experiments have shown that the chromatin fiber is a highly dynamic entity with pronounced structural diversity that includes properties of idealized zig-zag and solenoid models, as well as other motifs. This diversity can produce a high packing ratio and thus inhibit access to a majority of the wound DNA. Despite much research, chromatin's dynamic structure has not yet been fully described. Long stretches of chromatin fibers exhibit puzzling dynamic behavior that requires interpretation in the light of gene expression patterns in various tissue and organisms. The properties of chromatin fiber can be investigated with experimental techniques, like in vitro biochemistry, in vivo imagining, and high-throughput chromosome capture technology. Those techniques provide useful insights into the fiber's structure and dynamics, but they are limited in resolution and scope, especially regarding compact fibers and chromosomes in the cellular milieu. Complementary but specialized modeling techniques are needed to handle large floppy polymers such as the chromatin fiber. In this review, we discuss current approaches in the chromatin structure field with an emphasis on modeling, such as molecular dynamics and coarse-grained computational approaches. Combinations of these computational techniques complement experiments and address many relevant biological problems, as we will illustrate with special focus on epigenetic modulation of chromatin structure.