[en] A set of metabolite carriers operates the traffic of numerous molecules consumed or produced in mitochondrial matrix and/or cytosolic compartments. As their existence has been predicted by the chemiosmotic theory, the first challenge, in the late sixties, was to prove their presence in the inner mitochondrial membrane and to describe the various transports carried out. The second challenge was to understand their mechanisms by the kinetic approach in intact mitochondria (seventies). The third challenge (late seventies-eighties) was to isolate and to reconstitute the carriers in liposomes in order to characterize the proteins and to establish the concept of a structural and a functional family as well as some structure-function relationship with the help of primary sequences. Genetics, molecular biology and genomic sequencing bring the fourth challenge (nineties): a raising number of putative carriers becomes known only by their primary sequences but their functions have to be discovered. The actual challenge of the future is the elucidation of the ternary structure of carrier proteins that together with site-directed mutagenesis and kinetic mechanism will permit to advance in the understanding of molecular mechanisms of transport processes.