The animal mitochondrial genome, although small, can have a big impact on health and disease. Non-pathogenic sequence variation among mitochondrial DNA (mtDNA) haplotypes influences traits including fertility, healthspan and lifespan, whereas pathogenic mutations are linked to incurable mitochondrial diseases and other complex conditions like ageing, diabetes, cancer and neurodegeneration. However, we know very little about how mtDNA genetic variation contributes to phenotypic differences. Infrequent recombination, the multicopy nature and nucleic acid-impenetrable membranes present significant challenges that hamper our ability to precisely map mtDNA variants responsible for traits, and to genetically modify mtDNA so that we can isolate specific mutants and characterize their biochemical and physiological consequences. Here, we summarize the past struggles and efforts in developing systems to map and edit mtDNA. We also assess the future of performing forward and reverse genetic studies on animal mitochondrial genomes. This article is part of the theme issue 'Linking the mitochondrial genotype to phenotype: a complex endeavour'.