Language production involves the retrieval of information from memory, the planning of an articulatory programme, and executive control and self-monitoring. These processes can be related to the domains of long-term memory, motor control, and executive control. Here, we argue that studying neuronal oscillations provides an important opportunity to understand how general neuronal computational principles support language production, also helping elucidate relationships between language and other domains of cognition. For each relevant domain, we provide a brief review of the findings in the literature with respect to neuronal oscillations. Then, we show how similar patterns are found in the domain of language production, both through review of previous literature and novel findings. We conclude that neurophysiological mechanisms, as reflected in modulations of neuronal oscillations, may act as a fundamental basis for bringing together and enriching the fields of language and cognition.