The eukaryotic cell genome has a multilevel regulatory system of gene expression that includes stages of preliminary activation of genes or of extended genomic regions (switching them to potentially active states) and stages of final activation of promoters and maintaining their active status in cells of a certain lineage. Current views on the regulatory systems of transcription in eukaryotes have been formed based on results of systematic studies on a limited number of model systems, in particular, on the α- and β-globin gene domains of vertebrates. Unexpectedly, these genomic domains harboring genes responsible for the synthesis of different subunits of the same protein were found to have a fundamentally different organization inside chromatin. In this review, we analyze specific features of the organization of the α- and β-globin gene domains in vertebrates, as well as principles of activities of the regulatory systems in these domains. In the final part of the review, we attempt to answer the question how the evolution of α- and β-globin genes has led to segregation of these genes into two distinct types of chromatin domains situated on different chromosomes.