In this review, the available data on whole genome duplication in different phylogenetic lineages of animals are summarized, and possible mechanisms of the genome duplication and its role in the evolution of animals are considered. Special attention is paid to the problems of studying the first stages of the genome evolution after its duplication and to the search for species the study of which will make it possible to identify the peculiarities of the genome diploidization process after its duplication. A group of species of free-living flatworms from the Macrostomum genus is suggested as a promising model object for such studies. According to our data, the genomes of some Macrostomum members (M. lignano, Macrostomum sp. 8) are a result of recent genome duplication and subsequent chromosome rearrangements. In addition, the peculiarities of morphology, life cycle, small genome size, and simply organized karyotype make Macrostomum almost an ideal model object for studying the early stages of duplicated genome reorganization.