Although it has been known for half a century that unique structures evolved in the cerebellum of anthropoid apes and became greatly enlarged in the human brain, the function of these structures still remains unknown. In an attempt to explain their function, a new concept of cerebellar capabilities is proposed, which is based both on neural evidence and on information-processing theory. The phylogenetically newest structures of the cerebellum may contribute to mental skills in much the same way that the phylogenetically older structures contribute to motor skills. In both cases, the cerebellum can send signals from the dentate nucleus to the cerebral frontal cortex via the thalamus. Signals from the older part of the dentate nucleus certainly help the frontal motor cortex to effect the skilled manipulation of muscles, and signals from the newest part of the dentate nucleus may help the frontal association cortex to effect the skilled manipulation of information or ideas. How such mental skills could have evolved in higher primates in the course of phylogenetic and ontogenetic development is shown. The validity of this new concept of cerebellar function can be tested on humans by means of tomographic brain scans.