With the advent of brain-imaging tools has come a renewed interest in the neurocognition of language. However, most of the currently used imaging tools do not have sufficient temporal resolution to capture language processing as it occurs over time. One method that does provide adequate temporal resolution involves recording event-related brain potentials (ERPs) from the scalp. ERPs reflect the summed, simultaneously occurring postsynaptic activity in large groups of neocortical pyramidal neurons. In our lab, we have used ERPs to learn more about language processing in native speakers and to track changes in brain activity that accompany the earliest stages of second-language learning. I will discuss the relevance of these data for the current debate over whether competence with a human language fundamentally reflects the acquisition and use of grammatical rules, or the gradual accrual of information about the statistical regularities in the linguistic input.