This work reviews current theoretical approaches of biophysics and bioinformatics for the descrip tion of nucleosome arrangements in chromatin and transcription factor binding to nucleosomal organized DNA. The role of nucleosomes in gene regulation is discussed from the molecular mechanistic and biologi cal points of view. In addition to classical problems in this field, actual questions of epigenetic regulation are discussed. The authors selected for discussion what seem to be the most interesting concepts and hypotheses. Mathematical approaches are described in a simplified language to attract attention to the most important directions of this field.