Externally, vertebrates are bilaterally symmetrical; however, left-right asymmetry is observed in the structure of their internal organs and systems of organs (circulatory, digestive, and respiratory). In addition to the asymmetry of internal organs (visceral), there is also functional (i.e., asymmetrical functioning of organs on the left and right sides of the body) and behavioral asymmetry. The question of a possible association between different types of asymmetry is still open. The study of the mechanisms of such association, in addition to the fundamental interest, has important applications for biomedicine, primarily for the understanding of the brain functioning in health and disease and for the development of methods of treatment of certain mental diseases, such as schizophrenia and autism, for which the disturbance of left-right asymmetry of the brain was shown. To study the deep association between different types of asymmetry, it is necessary to obtain adequate animal models (primarily animals with inverted visceral organs, situs inversus totalis). There are two main possible approaches to obtaining such model organisms: mutagenesis followed by selection of mutant strains with mutations in the genes that affect the formation of the left-right visceral asymmetry and experimental obtaining of animals with inverted internal organs. This review focuses on the second approach. We describe the theoretical models for establishing left-right asymmetry and possible experimental approaches to obtaining animals with inverted internal organs.