The packing of the genomic DNA in the living cell is essential for its biological function. While individual aspects of the genome architecture, such as DNA and nucleosome structure or the arrangement of chromosome territories are well studied, much information is missing for a unified description of cellular DNA at all its structural levels. Computer modeling can contribute to such a description. We present here some typical approaches to models of the chromatin fiber, including different amounts of detail in the description of the local nucleosome structure. The main results from our simulations are that the physical properties of the chromatin fiber can be well described by a simplified model consisting of cylinder-like nucleosomes connected by flexible DNA segments, with a geometry determined by the bending and twisting angles between nucleosomes. Randomness in the local geometry - such as random absence of linker histone H1 - leads to a dramatic increase in the chromatin fiber flexibility. Furthermore, we show that chromatin is much more flexible to bending than to stretching, and that the structure of the chromatin fiber favors the formation of sharp bends.