Mitochondria are obligate organelles of most eukaryotic cells that perform many different functions important for cellular homeostasis. The main role of mitochondria is supplying cells with energy in a form of ATP, which is synthesized in a chain of oxidative phosphorylation reactions on the organelle inner membrane. It is commonly believed now that mitochondria have the endosymbiotic origin. In the course of evolution, they have lost most of their genetic material as a result of genome reduction and gene transfer to the nucleus. The majority of mitochondrial proteins are synthesized in the cytosol and then imported to the mitochondria. However, almost all known mitochondria still contain genomes that are maintained and expressed. The processes of protein biosynthesis in the mitochondria - mitochondrial translation - substantially differs from the analogous processes in bacteria and the cytosol of eukaryotic cells. Mitochondrial translation is characterized by a high degree of specialization and specific regulatory mechanisms. In this review, we analyze available information on the common principles of mitochondrial translation with emphasis on the molecular mechanisms of translation initiation in the mitochondria of yeast and mammalian cells.