Abstract: This paper discusses the following two questions: (1) It introduces the hypotheses and models of second language learning and processing with the evidence from cognitive neuroscience, including Critical Period Hypothesis, Declarative/Procedural Model, Shallow Structure Hypothesis and Unified Competition Model of language learning. On the basis of those, it presents their main ideas, predictions about the processes of second language learning and the evidence for and against these theories from cognitive neuroscience, especially ERP and fMRI. (2) It also discusses the debates among the theories so that it can lay a foundation for further experimental studies.