This review focuses on the import of processable precursor proteins into the mitochondrial matrix; the import of carrier proteins into the inner mitochondrial membrane is also briefly discussed. Post- and cotranslational theories of the import, specific features of the presequence structures, and effects of some cytosolic factors on the import of precursor proteins are reviewed. The data on the structure of the protein translocases of the outer (TOM complex) and the inner (TIM complex) membranes of mitochondria and the current models of the precursor protein import by these translocases are also summarized. © 2000 MAIK "Nauka/Interperiodica".