The dorsal pallium (a.k.a. the cortex in the mammals) makes a large loop circuit with the basal ganglia and the thalamus known to control and adapt behavior but the who's who of the functional roles of these structures is still debated. Influenced by the Triune brain theory that was proposed in the early sixties, many current theories propose a hierarchical organization on the top of which stands the cortex to which the subcortical structures are subordinated. In particular, habits formation has been proposed to reflect a switch from conscious on-line control of behavior by the cortex, to a fully automated subcortical control. In this review, we propose to revalue the function of the network in light of the current experimental evidence concerning the anatomy and physiology of the basal ganglia-cortical circuits in vertebrates. We briefly review the current theories and show that they could be encompassed in a broader framework of skill learning and performance. Then, after reminding the state of the art concerning the anatomical architecture of the network and the underlying dynamic processes, we summarize the evolution of the anatomical and physiological substrate of skill learning and performance among vertebrates. We then lay out our hypothesis that the development of automatized skills relies on the BG teaching cortical circuits and is actually a late feature linked with the development of a specialized cortex or pallium that evolved in parallel in different taxa. We finally propose a minimal computational framework where this hypothesis can be explicitly implemented and tested.