More than a century ago, Broca (1861), Wernicke (1874) and Lichteim (1885) laid the foundations for the first anatomo-functional model of language, secondarily enriched by Geschwind (1967), leading to the Broca-Wernicke-Lichteim-Geschwind model. This model included the frontal, parietal, and temporal cortices as well as a subcortical structure, which could be the striatum, whose nature and role have remained unclear. Although the emergence of language deficits in patients with striatal injury has challenged the cortical language models developed over the past 30 years, the integration of the striatum into language processing models remains rare. The main argument for not including the striatum in language processing is that the disorders observed in patients with striatal dysfunction may result from the striatal role in cognitive functions beyond language, and not from the impairment of language itself. Indeed, unraveling the role of the striatum and the frontal cortex, linked by the fronto-striatal pathway, is a challenge. Here, we first reviewed the studies that explored the link between striatal functions and the different levels of language (phonetics, phonology, morphology, syntax, and lexicosemantics). We then looked at the language models, which included the striatum, and found that none of them captured the diversity of experimental data in this area. Finally, we propose an integrative anatomofunctional model of language processing combining traditional language processing levels and some "executive" functions, known to improve the efficiency and fluidity of language: control, working memory, and attention. We argue that within this integrative model, the striatum is a central node of a verbal executive network that regulates, monitors, and controls the allocations of limited cognitive resources (verbal working memory and verbal attention), whatever the language level. This model combines data from neurology, psycholinguistics, and cognitive science.