Nuclear-mitochondrial DNA segments (NUMTs) are mitochondrial DNA (mtDNA) fragments that have been inserted into the nuclear genome. Some NUMTs are common within the human population but most NUMTs are rare and specific to individuals. NUMTs range in size from 24 base pairs to encompassing nearly the entire mtDNA and are found throughout the nuclear genome. Emerging evidence suggests that the formation of NUMTs is an ongoing process in humans. NUMTs contaminate sequencing results of the mtDNA by introducing false positive variants, particularly heteroplasmic variants present at a low variant allele frequency (VAF). In our review, we discuss the prevalence of NUMTs in the human population, the potential mechanisms of de novo NUMT insertion via DNA repair mechanisms, and provide an overview of the existing approaches for minimizing NUMT contamination. Apart from filtering known NUMTs, both wet lab-based and computational methods can be used to minimize the contamination of NUMTs in analyses of human mtDNA. Current approaches include: (1) isolating mitochondria to enrich for mtDNA; (2) applying basic local alignment to identify NUMTs for subsequent filtering; (3) bioinformatic pipelines for NUMT detection; (4) k-mer-based NUMT detection; and (5) filtering candidate false positive variants by mtDNA copy number, VAF, or sequence quality score. Multiple approaches must be applied in order to effectively identify NUMTs in samples. Although next-generation sequencing is revolutionizing our understanding of heteroplasmic mtDNA, it also raises new challenges with the high prevalence and individual-specific NUMTs that need to be handled with care in studies of mitochondrial genetics.