Interest in the intersection between bilingualism and cognitive control and accessibility to neuroimaging methods have resulted in numerous studies with a variety of interpretations of the bilingual cognitive advantage. Neurocomputational Emergentism (or Neuroemergentism for short) is a new framework for understanding this relationship between bilingualism and cognitive control. This framework considers Emergence, in which two small elements are recombined in an interactive manner, yielding a non-linear effect. Added to this is the notion that Emergence can be captured in neural systems (...) using computationally inspired models. This review poses that bilingualism and cognitive control, as examined through the Neuroemergentist framework, are interwoven through development and involve the non-linear growth of cognitive processing encompassing brain areas that combine and recombine, in symbiotic and parasitic ways, in order to handle more complex types of processing. The models that have sought to explain the neural substrates of bilingual cognitive differences will be discussed with a reinterpretation of the entire bilingual cognitive advantage within a Neuroemergentist framework incorporating its neural bases. It will conclude by discussing how this new Neuroemergentist approach alters our view of the effects of language experience on cognitive control. Avenues to move beyond the simple notion of a bilingual advantage or lack thereof will be proposed. (shrink)