Fundamental breakthroughs in the neurosciences, combined with technical innovations for measuring brain activity, are shedding new light on the neural basis of second language (L2) processing, and on its relationship to native language processing (L1). The long-held assumption that L1 and L2 are necessarily represented in different brain regions in bilinguals has not been confirmed. On the contrary, the available evidence indicates that L1 and L2 are processed by the same neural devices. The neural differences in L1 and L2 representations are only related to the specific computational demands, which vary according to the age of acquisition, the degree of mastery and the level of exposure to each language. Finally, the acquisition of L2 could be considered as a dynamic process, requiring additional neural resources in specific circumstances.