The increasing variability of phenotypic traits in agricultural animal species makes it necessary to search for reliable DNA markers. Due to the poor efficiency of using clustered single-nucleotide polymorphisms (SNP) and individual genomic elements, the hierarchy of gene regulatory networks has become a relevant research area. We summarized available information on different levels of epigenetic regulation, from the linear DNA sequence and its secondary and tertiary structures to the factors outside the cell nucleus, i.e., intercellular contacts and interactions with the extracellular matrix. We also discussed the features of genomic distribution and the role of topologically associated domains (TADs), and architectural protein CTCF in chromatin loop formation. CTCF mediates protein-protein interactions and interacts with various RNA variants. It also involved in epigenetic modifications of the DNA nucleotide sequence, a target of CTCF binding. Such targeted sites are located in transposable elements (TEs). As a result of the evolutionary conservation, they are also to be found in TAD, regardless of the fact that they are delivered by species-specific TEs. CTCF and its binding sites are known to affect the structure of the mitotic spindle. They also have a certain impact on cholesterol biosynthesis, which affects the plasma membrane and cell migration. CTCF indirectly participates in the variability of intercellular contacts and interactions with the extracellular matrix. In animals, CTCF and its binding targets are involved in all levels of gene regulatory networks that maintain or change genomic expression.