The understanding of the connection between malignant cell transformation and genetic instability has existed for a long time. Such markers of genetic instability as micronuclei (MN) and nuclear abnormalities - nucleoplasmic bridges (NPM) and nuclear buds are signs of malignant growth. However, they were seen only as a by-product of genetic instability, a convenient tool for its study for a long time. Only the studies of recent decades that used the latest methods of molecular genetic analysis (genome sequencing of an individual cell, long-term intravital microscopy and individual chromosomes labelling, hybridization in situ, etc.) have made it possible to establish that the rearrangements of the genetic material in cancer cells are much deeper and more massive than it thought to be. In addition, MN turned out to play an active role in maintaining the state of chromosomal instability in the cell population. This review outlines the current understanding of the processes leading to the emergence of unstable genomes - the phenomenon of «genomic chaos» and its particular case, chromothripsis. The molecular biological features of MN and their role in cellular life and the life of the whole organism are also considered. The significance of MN as diagnostic and prognostic indicators in oncological, neurodegenerative and many other diseases has been analyzed. Much attention is paid to the use of cytome analysis of peripheral blood lymphocytes and human epithelial cells in medical research. It has been suggested that, when used in medical research, cytome analysis can serve as a tool to identify individuals with higher cancer risk. We used the PubMed, Web of Science, ResearchGate, Scopus, eLibrary databases as the sources of literature.