The transition of detached fragments of mitochondrial DNA into the nucleus and their integration into chromosomal DNA is a special kind of genetic variability that highlights the relation between the two genomes and their interaction in a eukaryotic cell. The human genome contains several hundreds of insertions of mtDNA fragments (NUMTS). This paper presents an overview of the current state of research in this area. To date, evidence has been obtained that the occurrence of new mtDNA insertions in the nuclear genome is a seldom but not exceptionally rare event. The integration of new mtDNA fragments into the nuclear genome occurs during double-strand DNA break repair through the non-homologous end joining mechanism. Along with evolutionarily stable "genetic fossils" that were integrated into the nuclear genome millions of years ago and are shared by many species, there are NUMTS that could be species-specific, polymorphic in a species, or "private". Partial copies of mitochondrial DNA in the human nuclear genome can interfere with mtDNA during experimental studies of the mitochondrial genome, such as genotyping, heteroplasmy assessment, mtDNA methylation analysis, and mtDNA copy number estimation. In some cases, the insertion of multiple copies of the complete mitochondrial genome sequence may mimic paternal inheritance of mtDNA. The functional significance of NUMTS is poorly understood. For instance, they may be a source of variability for expression and splicing modulation. The role of NUMTS as a cause of hereditary diseases is negligible, since only a few cases of diseases caused by NUMTS have been described so far. In addition, NUMTS can serve as markers for evolutionary genetic studies. Of particular interest is the meaning of NUMTS in eukaryotic genome evolution. The constant flow of functionally inactive DNA sequences from mitochondria into the nucleus and its significance could be studied in view of the modern concepts of evolutionary theory suggesting non-adaptive complexity and the key role of stochastic processes in the formation of genomic structure.