A growing body of literature examining the neurocognitive processes of interpersonal linguistic interaction indicates the emergence of neural alignment as participants engage in oral communication. However, questions have arisen whether the study results can be interpreted beyond observations of cortical functionality and extended to the mutual understanding between communicators. This review presents evidence from electroencephalography (EEG) and functional near-infrared spectroscopy (fNIRS) hyperscanning studies of interbrain synchrony (IBS) in which participants communicated via spoken language. The studies are classified into: knowledge sharing; turn-taking speech co-ordination; cooperation, problem-solving and creativity; and naturalistic discussion paradigms according to the type of interaction specified in each study. Alignment predominantly occurred in the frontal and temporo-parietal areas, which may reflect activation of the mirror and mentalizing systems. We argue that the literature presents a significant contribution to advancing our understanding of IBS and mutual understanding between communicators. We end with suggestions for future research, including analytical approaches and experimental conditions and hypothesize that brain-inspired neural networks are promising techniques for better understanding of IBS through hyperscanning.