This paper aims to discuss old and contemporary perspectives in understanding language acquisition taking into account the neural theory of language. Discussing a recent theory by Kuhl (2010), neural substrates of first language learning will be put forward (Berwick et al., 2013). Neural substrates of phonetic learning, word learning, sentence processing, and syntax development are separately discussed. As a novel window to look into language learning in a greater detail, second language learning in relation to the theories of language acquisition is further discussed. Second language learning and dual vs. single coding structure relating to language acquisition are discussed in relation to the theories that have previously been explained. Finally, a discussion of contemporary issues in understanding both first and second language acquisition in relation to bilingualism is presented. In sum, investigating language acquisition requires a multi-disciplinary approach taking psychology, linguistics, and cognitive neuroscience of language into account is necessary.