This review centers on the neural mechanisms underlying the primate cognitive control of vocalizations, i.e. the capacity to regulate vocal productions in a goal-directed manner. In both human and non-human primates (NHPs), two main frontal brain regions are associated with top-down vocal control: a ventrolateral frontal region (VLF), comprising the ventrolateral prefrontal cortex and ventral premotor region; and a dorsomedial frontal region (DMF), comprising the mid-cingulate cortex, pre-supplementary and supplementary motor areas. These regions are cytoarchitectonically comparable across humans and NHPs and could serve generic functions in primate vocal control. Here, we first summarize the key anatomical properties of VLF and DMF regions as well as their involvements in the motor and cognitive control of vocalizations in both humans and NHPs. Finally, in light of the reviewed evidence, we discuss the existence of a primate VLF-DMF network and its generic functions in the cognitive control of vocalizations. We further suggest how this network and its functions may have changed across primate evolution to enable modern human speech.