Loss of mitochondrial function not only causes specific mitochondrial diseases but also contributes to serious conditions such as neurodegeneration and diabetes. Since mitochondrial DNA is transcribed as a polycistronic message comprised of three forms of RNA (rRNA, mRNA, and tRNA), proper 5′- and 3′-end cleavage is essential. In the nucleus, tRNA 5′-end processing is carried out by the first identified ribozyme, RNase P. In contrast, mitochondrial tRNAs are processed by a three-protein complex, mitochondrial RNase P, which does not have an RNA component. An accessory subcomplex made of the m1A9 methyltransferase MRPP1 and the dehydrogenase MRPP2 binds to the metallonuclease MRPP3 that cleaves the RNA phosphodiester backbone. Each protein has been shown to be essential in model organisms, and loss of each gives rise to human multisystemic diseases with many characteristics of mitochondrial disease. In this review, we discuss what is known about the mitochondrial RNase P complex, the molecular mechanism of 5′-end mitochondrial tRNA processing, and how loss of this activity causes human disease.